CMS NOTES de la SMC

Volume 34 No. 5 September/ Septembre 2002

In this issue / Dans ce numero´ DU BUREAU DU les liens avec l’industrie et defendu´ PRESIDENT´ le roleˆ des sciences mathematiques´ dans toute strategie´ d’innovation et Editorial...... 2 nous commenc¸ons a` en recueillir les fruits. Il est en effet plus NSERC Reallocation...... 3 facile de defendre´ notre discipline aupres` des organismes subvention- 2001 CMS Doctoral Prize . . . . . 5 naires. Les activites´ grand public que nous avons menees´ ces dernieres` Education Notes ...... 9 annees´ et plus particulierement` pen- dant l’annee´ mathematique´ mondi- Awards/Prix ...... 11 ale ont contribue´ a` redorer l’image des mathematiques´ aupres` des medias Book Review: Topics in Prob- et du public. Nous nous sommes ability and Lie Groups : raproches´ des milieux d’education´ et Boundary Theory ...... 12 nous pouvons esperer´ jouer un roleˆ de leadership en enseignement des Book Review: Backlund¨ and mathematiques´ au pays. Darboux transformations, Christiane Rousseau Nous devons cependant rester vig- the geometry of solitons . . . . 14 Premier message du president´ ilants car le ciel n’est pas sans nu- (English version on page 32) age. Comment va evoluer´ le monde CMS Winter Meeting 2002 des publications scientifiques? Ce sont ´ Reunion d’hiver de la SMC les revenus provenant de nos publica- 2002 ...... 19 C’est le premier message que je vous adresse a` titre de presidente´ de tions qui nous permettent de financer beaucoup de nos autres activites.´ Si Math In Moscow Update ...... 33 la Societ´ emath´ ematique´ du Canada. Graceˆ au travail et au devouement´ le marche´ des publications s’effondre nous devrons couper dans les bud- 34th Canadian Mathematical de centaines de membres de la gets alloues´ aux activites´ educatives,´ Olympiad Winners ...... 36 communautemath´ ematique´ canadi- enne depuis 57 ans la SMC est main- services electroniques´ ou activites´ de Obituary/Avis de dec´ es...... ` 39 tenant une grande societ´ e.´ De plus recherche. De plus, alors que beau- notre discipline est bien mieux po- coup de membres de notre commu- News from Departments ...... 40 sitionnee´ qu’il y a quelques annees.´ naute´ prennent leur retraite nous de- L’infrastructure de recherche est main- vons convaincre les jeunes recrues Calendar of events / Calendrier tenant tres` developp´ ee´ avec trois in- des universites´ canadiennes de devenir des ev´ enements.´ ...... 42 stituts et BIRS dont la program- membres de la Societ´ emath´ ematique´ mation scientifique couvre un large du Canada et de travailler avec nous. Rates and Deadlines / Tarifs et spectre de domaines des sciences Ech´ eances´ ...... 43 mathematiques.´ Nous avons resserre´ (continued on page 33) SEPTEMBER/SEPTEMBRE CMS NOTES

EDITORIAL Depuis l’invention de l’imprimerie a` CMS NOTES partir de caracteres` amovibles, il y a NOTES DE LA SMC six cents ans, et plus particulierement` depuis la creation´ des journaux et re- Les Notes de la SMC sont publiees´ vues, vers la moitiedudix-septi´ eme` par la Societ´ emath´ ematique´ du Canada siecle,` on tient pour acquis la diffu- (SMC) huit fois l’an (fevrier,´ mars, avril, sion de l’information sur un support mai, septembre, octobre, novembre et papier. Mais l’arrivee´ de l’ordinateur decembre).´ a tout chamboule.´ Les avancees´ tech- Redacteurs´ en chef nologiques associees´ a` l’ordinateur, Peter Fillmore; S. Swaminathan ainsi que les progres` realis´ es´ en traite- [email protected] S. Swaminathan ment de texte ont et´ etr´ es` avan- tageux pour le transfert electronique´ ´ ´ Since the invention of printing from Redacteur-gerant d’information technique ou scien- movable type about six centuries ago Graham P. Wright tifique. Les auteurs et les editeurs´ and more especially since the devel- Redaction´ font maintenant un usage poussedu´ opment of journals in mid-seventeenth Education´ : Edward Barbeau; traitement electronique´ aux etapes´ century, dissemination of information Harry White de la composition et de la revision´ through printing has been taken for [email protected] des articles de revues et des livres. granted. This situation changed with Reunions´ : Monique Bouchard Des logiciels permettent en outre de the advent of computers. The rise of [email protected] regler´ les problemes` complexes as- technology associated with them and Recherche : Noriko Yui socies´ a` la composition de problemes` progress in electronic processing of [email protected] ou de formules mathematiques,´ ainsi words have yielded enormous advan- Assistante alar` edaction´ que les diagrammes et les photogra- tages to scientific and technical infor- Victoria L. Howe phies. Un grand nombre de re- mation transfer. Electronic processing vues sont desormais´ offertes en version Note aux auteurs : indiquer la section is now used extensively by authors and electronique.´ Dernierement,` Springer choisie pour votre article et le faire par- publishers for composition and editing Verlag a annonce´ que sa collection venir aux Notes de la SMC a` l’adresse of journal articles and books. Software de Notes de conferences´ serait aussi postale ou de courriel ci-dessous : packages have been developed to han- offerte sous peu en version Web. dle complex mathematical typesetting Societ´ emath´ ematique´ du Canada Comme nous nous dirigeons vers un including diagrams and photographs. 577, rue King Edward monde de communication sans papier, Many journals have on-line versions C. P. 450, Succursale A nous devons examiner les profondes available now. Springer Verlag has Ottawa, Ontario, Canada K1N 6N5 repercussions´ qu’auront ces transfor- announced recently that their Lecture Tel´ ephone´ : (613) 562-5702 mations sur un grand nombre de per- Notes Series is also going on-line. As Tel´ ecopieur´ : (613) 565-1539 sonnes et d’organismes, y compris we move into a paperless communica- courriel : [email protected] les auteurs, les lecteurs, les editeurs´ tion environment we need to examine Site Web : www.smc.math.ca et les bibliotheques.` Asar` eunion´ its profound implications for many in- Les Notes,lesredacteurs´ et la SMC d’avril 2002 tenue a` Paris, le comite´ dividuals and institutions including au- ne peuvent etreˆ tenus responsables des executif´ de l’Union mathematique´ in- thors, users, publishers and libraries. opinions exprimees´ par les auteurs. Les ternationale a approuve´ des recom- The International Mathematical fichiers d’option de style utilises´ pour mandations concernant l’information Union Executive Committee has ap- la production de ce volume sont une et la communication electroniques.´ Le proved recommendations on electronic version modifiee´ des fichiers conc¸us comite´ a dresse´ une liste de pra- information communication at their par Waterloo Maple Software,
c 1994, tiques exemplaires pour les per- meeting in April 2002 in Paris. They 1995. sonnes du domaine de la publica- have identified a number of ”best prac- tion d’ouvrages mathematiques.´ Les tices” for those involved with math- ISSN : 1193-9273 (imprime)´ recommandations portent sur toutes ematical literature. The recommen- 1496-4295 (electronique)´ les formes de publication scientifique. dations concern all forms of schol- c Societ´ emath´ ematique´ du Canada Ailleurs dans les NOTES, vous trou- arly publishing. A brief announcement 2002 verez une breve` annonce acesujet` concerning this is included elsewhere ainsi qu’une adresse electronique´ ou` in this issue of the NOTES with a URL vous pourrez obtenir plus de details.´ reference for detailed information.

2 NOTES de la SMC SEPTEMBER/SEPTEMBRE

NSERC REALLOCATION EXERCISE 2000-2002

Every four years, up to 10% of NSERC’s Research Grants Richard Kane (UWO), Chair Program budget is redistributed according to the changing Hershy Kisilevsky (Concordia) needs and priorities of the Canadian scientific research com- Robert Moody (BIRS/Alberta) munity. In addition to the effect this has on the individ- Richard Nowakowski (Dalhousie) ual Grant Selection Committee (GSC) budgets, it influences Edward Vrscay (Waterloo). planning in the disciplines and is useful in communicating the importance of scientific research in Canada. The members of the NSERC Reallocations Committee are: In each discipline the GSC establishes a Steering Com- Robert Birgenau (University of Toronto) mittee, which consults the community and prepares a sub- Elizabeth Cannon (University of Calgary) mission to NSERC’s Reallocations Committee. The steering Michael Fryzuk (UBC) committees were set up in the summer of 2000 and their re- Brian Hall (Dalhousie University) ports were due in January 2002. NSERC’s funding decisions Barbara Keyfitz (University of Houston) were released in July (see the President’s report and the re- Larry Mayer (University of New Hampshire) port by the Steering Committee Chair, Richard Kane, in this Peter Nicholson (BCE Inc.) ´ issue). Robert Papineau (Ecole de technologie superieure)´ David Schindler (University of Alberta) David Turpin (University of Victoria) The Steering Committee for Pure and Applied Mathematics Sidney Wolff (National Optical Astronomy Observatories) has the following members: James Arthur (Toronto) The Committee is chaired by Gilbert Drouin (NSERC Coun- cil, Valorisation-recherche Quebec).´ Peter Borwein (SFU) Ken Davidson (Fields Institute/Waterloo) Michel Delfour (Montreal)´ The CMS Notes plans to publish the submission of the Nassif Ghoussoub (PIMS/UBC) pure and applied mathematics Steering Committee in instal- Katherine Heinrich (Regina) ments. The first of these follows, consisting of the introduc- Jacques Hurtubise (CRM/McGill) tion and the first two parts.

Report of the Steering Committee for Pure and Applied Mathematics

Mathematics in Canada is represented posals on both excellence and the fu- nity; Part 4 provides an overview of the by an energetic and cohesive commu- ture: namely, on top researchers, to- 3 mathematical institutes; Part 5 is a nity with international impact, a very morrow’s leaders, and new applicants. report on new initiatives in infrastruc- effective infrastructure for the support Our proposals will request the follow- ture; Part 6 addresses the training of and dissemination of research (through ing: highly qualified personnel (HQP); Part its 3 mathematical institutes and their (1) Proposal A: targeted funding 7 provides further considerations on impressive initiatives), and a strong in- for recognized top researchers who can the funding proposals and the conse- volvement in cross-disciplinary activ- assume a leadership role involving an quences of no increased funding; and ities. In the past decade, Canadian active focused group; (2) Proposal B: Part 8 is an appendix containing de- mathematics has undergone a funda- targeted funding for younger emerg- tails concerning each of the mathemat- mental restructuring and has emerged ing leaders whose research and train- ical institutes. with a clear awareness of the disci- ing activities have moved to a higher Part 1: A Vision for Mathematics in pline’s central and pervasive role in level; and (3) Proposal C: adequate en- Canada Canadian society and of the urgent try grants for the very large number of need to fashion a strategy, built on junior and senior new applicants who A New Reality that reality, for the community. The will be applying to GSC 336/337 over The role and impact of the math- foundation for this activity is the sta- the next 4 years. ematical sciences within the global ble funding of individual researchers The document is structured as fol- scientific, technological, and biomed- and their research groups, the major- lows: Parts 1 and 2 provide the vi- ical enterprise has grown at an aston- ity of which is provided through GSCs sion and strategy for Canadian math- ishing rate over the past decade. The 336/337. ematics and the funding proposals for conceptual and computational tools To build on our momentum, we are achieving them; Part 3 is a report of mathematics have become essen- focusing our goals for the funding pro- on the Canadian mathematics commu- tial for progress in many areas of the

3 SEPTEMBER/SEPTEMBRE CMS NOTES life sciences, information and commu- has been a 20-year process, achieved Sciences Research Institute in Berke- nications technologies, nanosciences, through constant recruitment and de- ley (through NSERC, the NSF, and and financial and industrial sectors. velopment of talented new researchers. the Alberta government). BIRS will This is a new reality for mathemat- The current generation of younger re- provide Canadian mathematicians and ics. The interdisciplinary nature of searchers is internationally prominent users of mathematics with a major fo- mathematics and its “critical role in in many major areas. rum for research-intense workshops, advancing interdisciplinary research” Priorities promoting both mathematical research was stressed in the recent NSF (US and its interactions. The priorities of Canadian mathe- National Science Foundation) budget The mathematical institutes are a matics are: statement before the House Appro- vivid demonstration of the fact that (1) to strengthen its leadership in priations Committee. Mathematics many frontiers of knowledge are con- fundamental and interdisciplinary re- is a “powerful tool for insight and centrated in areas that cut across tradi- search, providing crucial mathematical a common language for science and tional disciplines, but possess mathe- resources for science and technology; engineering.” In what is described as matical tools as their common denom- and (2) to increase its capacity to re- a centerpiece of NSFs core invest- inator. Mathematics is the only disci- cruit, support, and train HQP in math- ments, the NSF proposed to double pline in Canada to have created such ematics. its funding for mathematical research large scale (and effective) institutions over the next few years. Canadian Mathematical Institutes for interdisciplinary activity. mathematics is fully engaged in this The presence of 3 mathematical in- Part 2: Strategy and Funding Pro- new reality. Over the past 10 years, stitutes capable of providing innova- posals Canadian mathematicians have forged tion and leadership in research is a The need for increased funding in substantial links to a broad spectrum major force behind the recent success mathematics is pervasive. In this pro- of scientific disciplines and emerging of Canadian mathematics. The re- posal, however, we limit our requests directions of research, and to financial search institutes in the mathematical to the case of certain key groups of and technological sectors. There is a sciences – Le Centre de Recherches researchers. In the last Reallocation need to maintain such momentum. The Mathematiques´ (CRM), the Fields In- Exercise, taking this approach proved full participation of Canadian science stitute for Research in Mathematical highly effective in advancing mathe- and technology in this highly math- Sciences (Fields), and the Pacific In- matical research and training. ematical and interdisciplinary world stitute for the Mathematical Sciences can be achieved only with a strong (PIMS)– have had a tremendous in- Implementation of Previous Proposals force of mathematically-literate and fluence on the Canadian mathematical The 1998 Reallocation Committee mathematically-sophisticated scien- community. The institutes have or- provided resources to GSCs 336/337 tists. The training of HQP in mathe- ganized numerous scientific programs for two categories of researchers: matics is a high priority. in major areas of current research, $539K for new applicants and younger A Strong Discipline with emphasis on outreach, interdis- researchers, and $323K for top re- Mathematics is a rich and active ciplinary, and international activities. searchers. This infusion of funding science with its own internal dynam- They have led the way in building has had a significant impact on a large ics and its own sources of fundamental bridges between Canadian mathemat- number of researchers and on the train- problems and conjectures in addition ics and other disciplines, and have ing of HQP. The following 3 statis- to being a conceptual framework and acted as major training centres for tics convey this impact and demon- source of powerful tools for science young talent. The institutes have also strate where much of these allocated and technology. The long-term im- pioneered the building of partnerships funds were applied: (i) there was an portance and relevance of mathemat- between Canadian mathematicians and increase in the number (from 32 to 59) ics to scientific endeavor as a whole the industrial and financial world. As of mathematicians with grants of $30K has been shown, over and over again, part of this activity, they brought to- or larger (i.e., roughly twice the aver- to be based on the strength and vigour gether researchers from mathemati- age grant in GSCs 336/337) in the pe- of its own core research. Furthermore, cal sciences and industry to form riod 1997/2001. In the process, these the ability of Canadian mathematics the national network, MITACS, and 59 mathematicians received an extra to participate in the greatly expand- the Montreal-based network, NCM2. $570K of funding, as the total value ing role of the mathematical sciences The most recent institute innovation of their grants rose from $1.6M to is necessarily founded on the quality is the Banff International Research $2.17M; of its researchers. The rise of Cana- Station (BIRS), a collaboration be- dian mathematics to its current level tween PIMS and the Mathematical (continued on page 37)

4 NOTES de la SMC SEPTEMBER/SEPTEMBRE

The Distribution Factor of Values of the Summatory Function of the Mobius¨ Function by Nathan Ng (Universite´ de Montreal)´

This note summarizes the part of my CMS doctoral prize lec- for all x>1. Mertens based this conjecture on a numerical ture that focussed on the summatory function of the Mobius¨ calculation of M(n) for n =1...10000. A related conjec- function. The lecture was titled “Limiting distributions and ture, known as the weak Mertens conjecture, asserts that zeros of Artin L-functions” and was presented in Toronto at   2 X M(x) the CMS Winter meeting in December 2001. dx log X. (5) I wish to thank the Canadian Mathematical Society for 1 x the honour of being chosen as the recipient of the 2001 CMS Each of these conjectures imply the Riemann hypothesis and doctoral prize. I would like to thank my supervisor, Profes- the simplicity of all of the zeros of ζ(s). For a time, it was sor David Boyd, who diligently guided me, generously gave believed that the bounds (4),(5) were true. However, Ingham of his time, and shared of his extensive knowledge of mathe- [In] dispelled the notion that (4) could be true with a condi- matics. tional proof that The summatory function of the Mobius¨ function − 1 − 1 The Mobius¨ function is defined as the generating se- lim sup x 2 M(x)=∞ , lim inf x 2 M(x)=−∞ (6) x→∞ x→∞ quence for the reciprocal of the Riemann zeta function, that is, assuming certain statistical properties of the zeros of ζ(s). ∞ 1
µ(n) Following Ingham’s ideas, Odlyzko and te Riele [OR] proved = . (1) s unconditionally in 1986 that ζ(s) n=1 n − k − 1 − 1 This translates to µ(n)=( 1) if n = p1 ...pk is square- lim sup x 2 M(x) > 1.06 , lim inf x 2 M(x) < −1.009 . x→∞ free and µ(n)=0otherwise. The Mobius¨ function plays an x→∞ important role in the analytic theory of numbers. It is espe- The question we now address is what is the true behaviour cially important in sieve theory and in the method of mollifi- of M(x)? Odlyzko and te Riele write in their article that cation as initiated by Selberg in his study of the zeros of the “No good conjectures about the rate of growth of M(x) are Riemann zeta function on the critical line. known.” We first present the current state of knowledge re- By partial summation of (1), we obtain M(x)  garding . The best unconditional upper bound is 1 ∞ M(x) 3 − 1 = s s+1 dx (2) | | − 5 5 ζ(s) 1 x M(x) x exp( c log x(log log x) ) valid for Re(s) > 1 where
for some effective constant c. On the other hand, if the Rie- M(x)= µ(n) (3) mann hypothesis is false, then n≤x θ− is the summatory function of the Mobius¨ function. The iden- M(x)=Ω±(x ) tity (2) demonstrates the direct connection between the zeta function and M(x). Over the years, this function has been where θ =supRe(ρ) with ρ ranging over the non-trivial ze- much studied and speculated about. One reason for interest ros of ζ(s) and any >0. Also observe that the existence in M(x) is that the Riemann hypothesis is equivalent to the of a multiple zero would drastically change the expected be- bound   haviour of M(x). For example if Θ+iγ were a multiple zero 1 log x of order m ≥ 1 then |M(x)|x 2 exp c log log x Θ m−1 for an effective constant c and any >0. Moreover, Stieltjes M(x)=Ω±(x log x) . and Mertens conjectured

1 Since we have some understanding of the behaviour of M(x) | |≤ 2 M(x) x (4) in these unlikely scenarios we assume the opposite is true.

5 SEPTEMBER/SEPTEMBRE CMS NOTES

3 Namely, we assume the Riemann hypothesis is true and that for k>− 2 where all zeros of the zeta function are simple. This is the most in-     k2
∞  2 teresting case to consider and also the more difficult case. It − 1 Γ(m + k) −m 4 ak = 1 p is currently known [C] that at least 10 of the zeros are simple p p m=0 m!Γ(k) and lie on the critical line. Our main interest in this problem originated with a com- and G is Barnes’ function defined by   ment of Heath-Brown [HB]. He writes, “It appears to be an z 1 2 2 G(z +1)=(2π) 2 exp − (z + γz + z) open question whether 2 − 1 ∞  n x 2 M(x) z −z+z2/2n 1+ e . n has a distribution function. To prove this one would want n=1 to assume the Riemann hypothesis and the simplicity of the This conjecture has been proven for k =0by Von Mangoldt zeros, and perhaps also a growth condition on M(x).” The and for k =1by Gonek assuming the Riemann hypothesis. key point is to construct a distribution function (probability In the case k =2the author has proven that the Riemann hy- measure) that demonstrates the properties of M(x). Our ap- pothesis implies this is the correct order of magnitude with proach to this problem is to exploit the connection between explicit upper and lower bounds. As for the negative mo- M(x) and negative discrete moments of the Riemann zeta ments, less is known. Gonek established a conditional proof 3 function. that J−1(T ) T and also conjectured that J−1(T ) ∼ π3 T Discrete moments of the Riemann zeta function which agrees with (8). Inverting equation (2) (by Perron’s formula) we have The idea of using Jk(T ) to study M(x) was first real-  1 c+i∞ xs ized by Gonek who makes use of these connections to study M(x)= ds 2πi c−i∞ sζ(s) M(x) in short intervals [Go2]. In order to obtain any in- formation about M(x), it is necessary to understand Jk(T ). where c>1 and x/∈ Z. Moving the contour to the left, it Without any knowledge of Jk(T ), no new information con- follows that cerning M(x) can be gleaned.
xρ M(x)=
+ E(x, T ) The limiting distribution ρζ (ρ) |γ|≤T The main theorem in [Ng2] is the construction of the lim- where E(x, T ) is a suitable error term. This last identity iting distribution of the function makes it clear that information concerning the sum − y y
e 2 M(e ) .
2k Jk(T )= |ζ (ρ)| 0<γ

  2 The problem in extending [RS] is that there is little uncon- 2 (k+1)
G (k +2) T T ditional information concerning ζ (ρ)−1. Thus it was neces- Jk(T ) ∼ ak log (8) G(2k +3) 2π 2π sary to assume bounds for the sum J−1(T ) as suggested in

6 NOTES de la SMC SEPTEMBER/SEPTEMBRE equations (7),(8) . The key lemma was proven by using tech- where B is any Borel set in R. Consequently, ν maybestud- niques from Cramer´ [Cr] in conjunction with J−1(T ) T . ied via X. Moreover, by assuming the linear independence 3+ (It should be noted that the trivial bound is J−1(T ) T conjecture and the assumptions of Theorem 1, we may com- and this is not sufficient to obtain any significant results re- pute the Fourier transform of ν exactly. It equals   garding M(x).)  ∞  −iξt 2ξ ν (ξ)= e dν(t)= j0 In a similar vein, we can prove bounds for M(x) or aver- | 1
1 | −∞ γ>0 ( 2 + iγ)ζ ( 2 + iγ) ages of M(x). Theorem 2 The Riemann hypothesis and J−1(T ) T where
∞ m z 2m (−1) ( 2 ) imply the weak Mertens conjecture in the form j0(z)= (m!)2     m=0  X 2
M(x) ∼ 2 is a Bessel function of order zero. Furthermore, by pursuing dx |
|2 log X (10) 1 x γ>0 ρζ (ρ) ideas of Montgomery [M] concerning sums of independent random variables we can show that for large V and 4 c2 − 1 3 5 ∞ 1 3 exp( c V exp(c V )) ν([V, )) 2 2 4 M(x) x (log log x) (11) c5 exp(−c4V exp(c6V 5 )) except on a set of finite logarithmic measure. (The exponent for effective constants ci > 0 for i =1...6. These argu- 3 5 2 in (11) may be reduced to 4 under the additional assump- ments assume the Riemann hypothesis, the linear indepen- 1 tion J− 1 (T ) T (log T ) 4 .) dence conjecture and bounds for both J 1 (T ) and J−1(T ). 2 − 2 Speculations on the lower order An analysis of these bounds suggest the following conjec- We now illustrate how Theorem 1 is useful for studying ture: the distribution of values of M(x). Suppose Theorem 1 were Conjecture There exists a number B>0 such that true for the indicator function of the set [V,∞). Equation (9) M(x) ± would then read limx→∞ √ 5 = B. (14) x(log log log x) 4 1 y − y lim meas{y ∈ [0,Y] | M(e )e 2 ≥ V } = ν([V,∞)) . After the completion of this work, I learned from Gonek that Y →∞ Y (12) he had an argument to suggest this lower bound 20 years ago. Apparently the heuristic argument in [Ng2] of the lower This indicates that the distribution of values of M(x) is re- bound (14) is similar to Gonek’s, however it was discovered lated to the tail of the probability measure ν. It is noted in independently. [RS] that identity (12) would be true if ν is absolutely con- We note that in the prime number case, where M(x) is tinuous. In fact, we can show that ν is absolutely continuous replaced by ψ(x) − x, Montgomery [M] conjectures that the 1 if the following conjecture is true. corresponding B equals 2π . In this case, the value of B is Linear independence conjecture Assume the Riemann not so clear and remains an open problem. We remark that hypothesis. If the non-trivial zeros of ζ(s) are denoted as years earlier Good and Churchhouse [GC] had conjectured 1 ρ = 2 + iγ, then the positive imaginary ordinates γ are lin- that √ early independent over Q. M(x) 12 limx→∞ √ 1 = ± . Now consider the random variable x(log log x) 2 π
2 This was based on modelling µ(n) as a random sequence X(θ)= sin(2πθk) | 1
1 | supported on the squarefree integers and by “applying” the γ >0 ( 2 + iγk)ζ ( 2 + iγk) k law of the iterated logarithm. Although Good and Church- where θ =(θ1,θ2,...,) is an element of the infinite torus house’s argument seems promising it relies on the assump- T∞. We note that if P is the canonical probability measure tion that µ(n) behaves randomly. However, the Mobius¨ func- on T∞ then the linear independence conjecture implies tion is not a random sequence as it is connected directly to ζ(s)−1. Thus M(x) is determined by the zeros of ζ(s) or −1 ν(B)=P (X (B)) more precisely by the discrete moments J 1 (T ),J−1(T ). − 2 7 SEPTEMBER/SEPTEMBRE CMS NOTES

Consequently, it is these negative moments that should de- demic Press, San Diego, (1989) 343-370 termine the behaviour of M(x). HKO C.P. Hughes , J.P. Keating , & N. O’Connell Ran- The author was supported in part by a grant from NSERC dom matrix theory and the derivative of the Rie- and NSF grant DMS 9729992. mann zeta function, Proceedings of the Royal So- References ciety (A), 456, (2000) 2611-2627 Co J.B. Conrey More than two-fifths of the zeros of the In A.E. Ingham On two conjectures in the theory of Riemann zeta function are on the critical line,J. numbers, Amer. J. Math., 64, (1942) 313-319 Reine Angew. Math, 399, (1989) 1–26 M H.L. Montgomery The zeta function and prime Cr H. Cramer´ Ein Mittelwertsatz in der Primzahltheo- numbers, Proceedings of the Queen’s Number rie, Math. Z., 12, (1922) 147–153 Theory Conference, Queen’s University, Kingston, Go1 S.M. Gonek On negative moments of the Riemann Ontario, (1980) 1-31 zeta-function, Mathematika, 36, (1989) 71–88 Ng1 N. Ng Limiting distributions and zeros of Artin L- Go2 —-The second moment of the reciprocal of the Rie- functions, Thesis, University of British Columbia, mann zeta-function and its derivative, notes from a (2000) talk presented at the MSRI, (1999) Ng2 —-The distribution of the summatory function of GC I.J. Good & R.F. Churchhouse The Riemann hy- the Mobius¨ function, (in preparation), pothesis and pseudorandom features of the Mobius¨ OR A.M. Odlyzko & H.J.J te Riele Disproof of the sequence, Math. Comp., 22, (1968) 857-861 Mertens conjecture, J. Reine Angew. Math, 357, HB D.R. Heath Brown The distribution and moments (1985) 138–160 of the error term in the Dirichlet divisor problem, RS M. Rubinstein & P. Sarnak Chebshev’s Bias,Ex- Acta. Arith., 60(4), (1990) 389-415 perimental Mathematics, 3, (1994) 173–197
Hej D. Hejhal On the distribution of log ζ (1/2+ T E.C. Titchmarsh The theory of the Riemann zeta it), Number Theory, Trace Formula, and Discrete function, second edition, Oxford University Press, Groups, Editor Aubert, Bombieri & Goldfeld, Aca- New York, (1986)

Best Practices in Electronic Scholarly Publishing

The Executive of the International The 15 “best practices” touch on time, and to archive material in formats Mathematical Union has endorsed a almost every area of scholarly elec- that have open standards. broad ranging set of recommendations tronic publication, and include such While the recommendations are on Electronic Information Communi- things as: aimed at the mathematical community, cation. – Suggestions to authors to version almost all apply to other scholarly dis- These recommendations, written their electronic preprints, to post them ciplines as well. by its Committee on Electronic In- on publicly available servers, and to The advice is meant to ease the formation and Communication (CEIC, become knowledgable about copyright transition in scholarly communication www.ceic.math.ca), suggest ways in – Advice to librarians to make deci- both for present scholars and for future which mathematicians, librarians, and sions based on journal price and pol- generations. publishers can help shape the future of icy, to be alert to the distinction be- scholarly communication. The com- tween posted and refereed papers, and The 15 specific recommendations mon principle used to formulate rec- to use web statistics with care will be updated in the future, and more ommendations is that those who write, – Encouragement to publishers to pro- detailed information will be added disseminate, and store mathematical vide key journal information (abstracts for each. The full text is available at literature should act in ways that serve and reference lists) without subscrip- www.ceic.math.ca/Best-Practices.pdf the interests of mathematics, first and tion, to make entire articles similarly or www.cms.math.ca/bulletins/Best- foremost. available after a suitable period of Practices.pdf

8 NOTES de la SMC SEPTEMBER/SEPTEMBRE

EDUCATION NOTES Ed Barbeau and Harry White, Column Editors

A new academic year which, since 1982, has addressed topics and themes of inter- est in undergraduate mathematics, opens with four introduc- The Education Notes are a regular feature of this news mag- tory essays written by Benoit Mandelbrot (the first in com- azine, and is intended to be a clearing house for information pany with Michael Frame) that argue for the historical sign- about primary, secondary and tertiary education that is of in- ficance of fractals and dynamical systems and their impor- terest to members of the Society. Accordingly, we hope that tance in achieving worthwhile goals of modern education and you will send us news about developments in your part of avoiding the abuses of the past. the country. In particular, is there innovative work in edu- cation going on in your department? Are there reports that In twenty years, the topics discussed in this volume have should be given national attention? Have you or any of your proved to be more than a flash in the pan. They not only colleagues received a teaching award? Do you have opin- excite the wonder and imagination of pupils, but are surpris- ions on any matters raised in the Notes? Please send your ingly accessible. Their newness allows novices to make dis- contributions to E.J. Barbeau, Department of Mathematics, coveries of their own, although this area certainly generates University of Toronto, Toronto, ON M5S 3G3 or by email to its share of intractable problems. In the third essay, Mandel- [email protected]. brot decries the cleavage between science and the arts, and hopes that fractals may be one tool to help resuscitate the Fractals and Education liberal ideal of citizens conversant and appreciative of sci- Book review ence. He has harsh words, not only for traditional mathemat- ics education rooted in the past, but for the New Maths of the Fractals, Graphics & Mathematics Education 1960s. He deplores the pegging of mathematical and scien- Benoit Mandelbrot & Michael Frame (editors) tific needs to purely utilitarian goals, and foresees the failure Mathematical Association of America of this approach to either be politically effective or share the 204 pp.; paperbound, 2002 beauty and creativeness of mathematics. In the fourth essay, ISBN 0-888385-169-5 (US$ 39.95) treating mathematics and society in the twentieth century, Mandelbrot discusses the special historical and social factors With respect to how we look at our discipline, one of the responsible for accentuating certain mathematical trends and most important developments of the last half century is the supressing others, but sees current mathematics as enjoying blossoming of the areas of fractals and dynamical systems. the health of diversity and constructive turmoil. Although their roots go back to the nineteenth century, their recent growth depends on two factors, one technical and the A dozen essays provide testimonials and descriptions of other ideological. The advent of the modern computer gave how fractals and dynamical systems have transformed teach- us the power to make explorations hitherto thought impossi- ing from the senior elementary to undergraduate levels. The ble, but we also had to be willing to seriously engage rough- reader is provided with mathematical examples as well as de- ness as well as smoothness and the notion that complexity scriptions of activities, assignments and projects. and unpredicability could result from simple inputs, as well as ascribe to experimentation a respectable place in mathe- An article by Ron Lewis of Sudbury is of particular in- matical practice. terest to Canadians. Inspired by a 1987 pilot project for high school students conducted by Brian Kaye of Lauren- This striking new mathematics occurs at a time when the tian University, Lewis created an advanced level Grade 12 teaching of mathematics in our schools, colleges and uni- credit course. I was aware of this course when I established versities is ripe for a revolution. Traditional instruction has a course in dynamical systems at the University of Toronto a mathematics as a sequential body of material owned (at best) dozen years ago. While my course made more use of alge- by the teacher to be parcelled out to the students. To avoid braic tools, that of Lewis explored the concept of dimension having the curriculum sink under the dead weight of the past, through observations, experiments and simulations (using gi- it will be necessary for teachers to bring in their pupils as ac- ant pumpkins, crumpled paper, electrolytic deposits, diffu- tive participants in the enterprise, to equip them to discharge sion, pancakes on a griddle). the responsibility of attending to their own learning, and to selectively ensure that they are provided with the core knowl- A useful article by Kenneth Monks describes how edge and techniques to attain facility. courses on fractals and chaos can be designed for many dif- ferent audiences and offers advice on textbooks, websites, This volume, number 58 in the series of MAA Notes software and hardware. Other essays discuss how the essence

9 SEPTEMBER/SEPTEMBRE CMS NOTES of these areas can be conveyed to non-science students and are prepared for the demands of a first year undergraduate those taking introductory courses; art has a useful role to course. Here are a few Canadian ones: play. www.math.unb.ca/#stud There are two appendices. The first introduces a conway.math.unb.ca/Placement/test “panorama”, which is a kind of index to the diverse uses of math.usask.ca/readin/menu.html fractals. Only two examples are provided in the text; for the www.mast.queensu.ca/diagnostic.html others, the reader has to visit the website //www.maa.org/Fractals/ Panorama/Welcome.html. [I was As part of an Australian Mathematical Methods Com- unable to reach this; however, I found a Yale University site puter Algebra Systems (CAS) pilot study, there is quite a nice through a Google search on Fractals/Panorama.] The sec- collection of problems on graphing. Consult the site: ond index includes reports of activities that high school and www.vcaa.vic.edu.ca/vce/studies/MATHS/caspilot.htm college teachers, who attended summer workshops, did with [If your search software is persnickety, try their classes. This is a fine initial handbook for those who www.edfac.unimelb.edu.au/DSME/CAS-CAT/proj.html wish to teach courses in this vital and fast-developing area. or enter via a Google search on caspilot. Look for the section The publication may be obtained from The Mathemat- entitled Sample examination papers.] My own experience ical Association of America, PO Box 91112, Washington, suggests that if students are fluent in handling inequalities DC 20090-1112 ( www.maa.org). The catalogue number is and sketching graphs, then they are probably in pretty good NTE-58. shape to handle the technical demands of a first calculus course.

RAND Mathematics Project Teaching Award at RMC

The RAND Corporation has set up a study panel to har- On May 17, 2002, at Convocation of the Royal Mili- ness the expertise of a variety of professionals to bring about tary College in Kingston, Minister of National Defence, Art an improvement in the general mathematical proficiency of Eggleton, congratulated the recipient of the Class of 1965 Ex- the citizenry. This panel, chaired by Deborah Loewenberg cellence in Teaching Award, David Wehlau of the mathemat- Ball, has posted a draft (dated March, 2002) of its report ics department. He was selected from a number of student Mathematical Proficiency for All Students: towards a strate- nominations by a Class of 1965 representative in consulta- gic research development program in mathematics educa- tion with nominators, department heads and deans. Along tion. This can be found on the site with a cash prize of $5000, the recipient receives a certificate www.rand.org/multi/achievementforall/math/index.html. and a plaque and is invited to give a public lecture. Would anyone be interested in reviewing this for the CMS Notes? The award will be actually presented in the fall, when Dr. Wehlau lectures to the public on the history and significance Websites for matriculants of cryptography. Students praised his enthusiasm, sense of humour, accessibility and clarity of explanation. In addition While educationists wrangle over what can and should to teaching his regular classes, he has supervised 18 under- be done in the high school curriculum, thanks to the net, it is graduate projects during the last decade. He received his un- possible for any student serious about taking a mathematics- dergraduate degree from the University of Western Ontario related program at college or university to take matters into in 1983 and his doctorate from Brandeis University in 1989. her own hands. There are many universities posting sam- He is currently a full professor, and cross-appointed to the ple problems that high school students can try to see if they mathematics and statistics department of Queen’s University.

LAURENT SCHWARTZ 1915-2002 The mathematical community is deeply saddened at the news of the death of the world renowned French mathematician Laurent Schwartz, which occurred on July 4th, 2002. He was a brilliant student at Ecole Normale Superieure (rue d’Ulm). During World War II, he was in Clermont-Ferrand with other future founding members of the Bourbaki group, before joining the University of Nancy. His discovery of the theory of distributions is fully recognized by his being awarded the Fields Medal in 1950. His teaching in Ecole Polytechnique has left memorable traces for thousands of students, for whom the human qualities of Laurent Schwartz cannot be separated from his mathematics. Laurent Schwartz used to emphasize that his life held on three pillars: mathematics, political engagement and butterflies, as his autobiography (Un mathmaticien aux prises avec le sicle, Odile Jacob, 1997) amply demonstrates.

10 NOTES de la SMC SEPTEMBER/SEPTEMBRE

AWARDS / PRIX

Moody Wins Killam Prize Moody took up his first academic position at the Uni- versity of Saskatchewan in 1966 and joined the Department of Mathematical and Statistical Sciences at the University of Alberta in 1989. He has published 68 research papers and six books.

The Canadian Mathematical Society has twice bestowed honours on Dr. Moody. He received the inaugural Coxeter- James Prize in 1978, given annually to the most outstanding Canadian mathematician within 10 years of his or her de- gree. In 1995, he was given the highest honour awarded by the Society, the Jeffery-Williams Prize, for his outstand- ing contribution to mathematical research. Other awards and distinctions include the 1995 Gordin Kaplan Award for Excellence in Research, the highest research prize awarded by the University of Alberta; the 1966 Province of Alberta Five prominent Canadian scholars in the fields of law, phi- Science and Technology Award for Outstanding Research; losophy, information technology, mathematics and genetics and the 1998 Centre de Recherches de Mathematique/Fields´ have been honoured with the 2002 Killam Prizes, Canada’s Institute Prize. In 2000, he was granted the title Docteur most distinguished annual awards for outstanding career honoris causa at the Universite´ de Montreal;´ he is a Fellow achievement in social sciences, humanities, engineering, nat- of the Royal Society of Canada and an Officer of the Order ural sciences and health sciences. The awards to Harry of Canada. W. Arthurs, Ian Hacking, Nicolas D. Georganas, Robert V. Moody and Lap-Chee Tsui were announced by the Canada Council for the Arts, which administers the Killam program. Fields Institute Fellows Robert Moody’s research has been described as “a classic example of the fruitful interplay between mathematics and The Fields Institute Director, Kenneth R. Davidson, has an- physics that has been at the heart of major scientific advances nounced the names of the first Fields Institute Fellows. The since the time of Newton.” Born in England in 1941, Dr. names were approved at the Annual General Meeting in June. Moody is currently a Professor in the Department of Mathe- This is an honorary title which is conferred on certain in- matical and Statistical Sciences at the University of Alberta dividuals who have made outstanding contributions to the in Edmonton. He has recently been appointed as the first Fields Institute, its programs, and to the Canadian mathemat- Scientific Director of the newly-founded Banff International ical community. It is a lifetime appointment. Research Station for Mathematical Innovation and Discovery J. Arthur M. Goresky E. Muller (BIRS). E.Bierstone S. Halperin P. Nicholson After spending his high school years in Ottawa, D.Brillinger V. Jones J. Paldus Dr. Moody completed his B.A. at the University of A.Carty R. Kane N. Pippenger Saskatchewan in 1962 and received his M.A. (1964) and J. Chadam M. Kolster C. Riehm Ph.D. (1966) from the University of Toronto. His dissertation S. Cook F. Lalonde T. Salisbury contained the basis for what is considered one of his greatest D. Coxeter P. Lancaster L. Seco achievements, the Kac-Moody algebras, which he discovered G. Elliott W. Langford W. Shadwick independently from and simultaneously with Russian mathe- P. Fillmore J. Marsden M. Sigal matician Victor G. Kac. The Kac-Moody algebras have given J. Friedlander M. Milevsky V. Snaith rise to numerous applications in various fields of mathemat- A. George R. Moody J. Stewart ics and mathematical physics. By the mid-1980s, the Kac- Moody algebras and their offspring, Virasoro algebras, had In future years, there will be a call for nominations to emerged as the basic mathematical structure underlying su- appoint a few new Fields Institute Fellows each year at the perstring theory. The Kac-Moody algebras won him and Kac discretion of the Board. The new recipients of this honour the 1994-95 Eugene Wigner Medal. will be announced at the Annual General Meeting each year.

11 SEPTEMBER/SEPTEMBRE CMS NOTES

Behavior at Infinity Via Probability and Potential Theory Book Review by Patrice Sawyer, Laurentian University

There is a phrase by Ledrappier author gives to the definitions. A grad- which is particularly illuminating (not uate student with a good background Topics in Probability and Lie only about his contribution but about in probability and Banach spaces, or a Groups: Boundary Theory the whole book). “These notes illus- researcher wanting to learn about this edited by J. C. Taylor trate a theme of this workshop, namely subject would do well by reading this CRM Proceedings Vol. 28 that potential theoretic and probabilis- paper. It is easy to visualize this pa- AMS, 2001 tic objects are useful to describe the per as the basis of a “teaching seminar” 202 pp behaviors at infinity of hyperbolic and on that topic. The reviewer found the semi-hyperbolic spaces.” (and, this definition of Brownian Motion in that reviewer adds, other geometric struc- setup to be intriguing but well justified. tures). Alessandro Figa-Talamanca (An The preface by Taylor provides an application of Gelfand pairs to a prob- informative introduction to each of the lem of diffusion in compact ultramet- contributions. For this reason, the re- ric space) acknowledges 2 particularly viewer will only present his general important sources [2, 7]. His paper impression of each article. is concerned with the use of Gelfand The first of the articles in the pairs in connection with finite trees book under review is by Jean-Philippe to compute spherical functions. This Anker and Lizhen Ji (Heat kernel and leads to the computation of the proba- Green function estimates on noncom- bility associated with a natural random pact symmetric spaces. II). It is par- walk on finite trees under appropriate ticularly close to the reviewer’s heart. conditions. Although the reviewer is The authors nicely tie in the various more used to Gelfand pairs in the con- In the Preface, J. C. Taylor ex- questions associated with estimating text of symmetric spaces, he found this plains that while the book was ini- the growth of the heat kernel on a sym- paper particularly accessible and illu- tially intended as a loose proceedings metric space. While keeping an ex- minating. for a seminar he organized in 1992, it pository flavor and being a nice in- evolved into something quite different. troduction to their work ([1]), a new, The contribution of Yves Guiv- As a result, several of the papers in the and simpler, approach is explained. In arc’h (Compactifications of symmetric book under review contain results and the words of the authors: “The basic spaces and positive eigenfunctions of approaches which are more recent. In point of this note is that the analysis the Laplacian) is based on joint work particular, three of the papers are re- of spherical functions near the walls is with Ji and Taylor. This is a solid pa- lated, to various degrees, to the mono- very subtle, but the heat kernel behaves per which is less expository in nature graph [8] that Taylor published in 1998 nicely because it satisfies the parabolic than those of Evans, Figa-Talamanca with Yves Guivarc’h and Lizhen Ji. Harnack inequality.” The relationship or Ledrappier; in fact, a conjecture by These are the papers by Anker and Ji, of this paper to [8] comes from the ap- E. B. Dynkin (see [3]) is verified in the by Guivarc’h and by Taylor himself. plication of their results in the book. paper. It might even be a good idea The papers by presenters Steve Next follows a survey by Steven to start by reading the more accessible Evans and Franc¸ois Ledrappier are N. Evans (Local fields, Gaussian mea- contribution by Taylor. The list of ref- closest to being in tune with the ini- sures, and Brownian motion)onhis erences given is rather comprehensive. tial intent of this book along with the ground breaking work on Brownian Francois Ledrappier (Some asymp- article by Alessandro Figa-Talamanca motion in the context of local fields totic properties of random walks on who was a participant of the workshop (see in particular [4, 5, 6]). The author free groups) investigates random walks but did not present. asks the very natural question “What of free groups F with a finite set of The reviewer found the papers by is the right way to generalize such no- generators with a view of describing these 3 authors to be particularly ac- tions as Gaussian measures and Brow- properties of the harmonic measure at cessible for non-experts (a category he nian motion in this setup?” The pa- infinity. In the section “Notes and Ref- admits belonging to), this being partic- per is a solid introduction to the sub- erence”, the notion of homogeneous ularly true of the expositions of Evans ject not only because of the examples, tree is put in context. The paper is very and Figa-Talamanca. but also because of the justification the well structured and self-contained. It

12 NOTES de la SMC SEPTEMBER/SEPTEMBRE

is a also a solid excursion and a walk- compact Symmetric Spaces,Ge- [5] S. N. Evans. Equivalence and ing stick is recommended. A compre- ometric and Functional Analysis, perpendicularity of local field hensive list of references is given at the 1999, v. 9, n. 6, 1035–1091. Gaussian measures, Seminar on end. Stochastic Processes 1990 (Van- [2] P. Diaconis. Group representa- J. C. Taylor (The Martin compact- couver, BC, 1990) (E. Cinlar, ed) tions in Probability and Statistics, ification associated with a second or- Progr. Probab. vol. 24, Birhauser,¨ IMS Lecture Notes Monogr. Ser., der strictly elliptic partial differential Boston, MA, 1991, 173–181. vol. 11, Institute of Mathematical operator on a manifold M) develops a Statistics, Hayward, CA, 1988. self-contained proof of the Martin inte- [6] S. N. Evans. Local field Brown- gral representation theorem for general [3] E. B. Dynkin. Markov processes ian motion, J. Theoret. Probab. 6 elliptic operators on Riemannian man- and problems in analysis, Six Lec- (1993), no. 4, 817–850. ifolds. The approach is based on PDE tures Delivered at the International techniques rather than on axiomatic Congress of Mathematicians in [7] G. Letac. Les fonctions spheriques´ potential theory. The paper also dou- Stockholm, 1962, Amer. Math. d’un couple de Gelfand bles as a fairly gentle introduction to Soc. Transl. Ser. 2, vol. 31, Amer. symetrique´ et les chaˆınes de Martin boundaries and to some of the Math. Soc., Providence, RI, 963, Markov, Adv. in Appl. Probab. 14 material presented in [8]. 1–24. (1981), no. 2, 272–294. To summarize, these papers [4]S.N.Evans.Local field Gaussian present a good mixture of expository measures, Seminar on Stochastic [8] Yves Guivarc’h, Lizhen Ji and papers and more advanced articles. Processes 1988 (Gainesville, FL, J C. Taylor. Compactifications 1988) (E. Cinlar, K. L. Chung, R. of symmetric spaces, Progress References K. Getoor, eds) Progr. Probab. vol. in Mathematics, 156. Birkhauser¨ [1] J.-P. Anker, L. Ji. Heat Kernel and 17, Birhauser,¨ Boston, MA, 1989, Boston, Inc., Boston, MA, 1998. Green Function Estimates on Non- 121–160. xiv+284 pp.

MATH-NET LAUNCHED

The International Mathematical Union (IMU) has just The Math-Net Page is an enhanced version of a web page released Math-Net, a worldwide electronic informa- that originated in a project in Germany, targeted at establish- tion and communication system for mathematics; see ing a nation-wide information and communication system for http://www.math-net.org. mathematics departments. A tool for generating Math-Net Why is Math-Net needed? Today, almost every mathe- Pages as well as assistance is available at no charge at matics department or research institute offers information on http://www.math-net.org/Math-Net Page Help.html. the World Wide Web. But the content, structure, and pre- Mathematics departments around the world are currently set- sentation of these pages vary widely, making it difficult for ting up Math-Net Pages. users to navigate and find information. Math-Net is an alter- The Math-Net Pages are collected by the Math-Net ser- native way for academic departments and research institutes vice NAVIGATOR, see http://www.math-net.org/navigator, to present information about themselves and their programs that gathers the local information and makes it globally consistently. Math-Net has been designed to facilitate access available. Other services of this type are MPRESS, see to high quality mathematical information worldwide, both by http://mathnet.preprints.org, collecting information about human users and search engines. mathematical preprints, and PERSONA MATHEMATICA, A special feature of Math-Net is the Math-Net Page, a a search engine for mathematical researchers, see web portal for mathematics departments and institutes that http://www.mi.uni-koeln.de/Math-Net/persona mathematica. presents information in a standardized, well-structured, and easy-to-use format. Math-Net paves the way towards open and free exchange The Math-Net Page is an additional entry point to institu- of information within and for the international mathematics tional information, immediately accessible from the depart- community. In May 2000, the IMU adopted the Math-Net ment’s homepage, and not meant to replace it. Using this sec- Charter, see http://www.math-net.org/Charter/. The IMU’s ondary homepage, mathematicians, scientists, students, and Committee on Electronic Information and Communication the news media can easily find relevant data, such as staff, (CEIC) has issued a recommendation that universities and student programs, colloquia, seminars, and publications. institutes worldwide install a Math-Net Page.

13 SEPTEMBER/SEPTEMBRE CMS NOTES

Backlund¨ and Darboux transformations and the geometry of solitons Book Review by Niky Kamran, McGill University

of surfaces induced by line congruences. The most famous Backlund¨ and Darboux transformations, of these geometric transformations is the classical Backlund¨ the geometry of solitons transformation of pseudo-spherical surfaces, that is surfaces of constant negative Gaussian curvature. Consider a piece of edited by A. Coley, D. Levi, R. Milson, C. Rogers and P. 3 Winternitz a surface S in R of negative Gaussian curvature, given as X ⊂ 2 → 3 → CRM Proceedings Vol. 29 the image of an immersion : U R R :(u, v) X AMS, 2001 year (u, v). If the coordinates (u, v) are chosen as the arc length 436 pp parameters along the asymptotic lines of S, then the neces- sary and sufficient condition for S to be of constant negative 1 Gaussian curvature K = − c2 is given by the celebrated sine- Gordon equation 1 θuv = sin θ, (1) c2 where θ(u, v) denotes the angle between the asymptotic lines at the point X(u, v) of S. The first and second fundamental forms of S are thus given by

I = du2 + 2 cos θdu dv + dv2, (2) 2 II = sin θdudv. (3) c Suppose that we are given a non-zero solution θ(u, v) of the sine-Gordon equation (1) and consider the over-determined The book under review is the proceedings of an AARMS- system of first-order partial differential equations for an un-  CRM Workshop on Backlund¨ and Darboux transformations known function θ (u, v), given by and the geometry of solitons, which was held in Halifax,     2β θ + θ  2 θ − θ Nova Scotia, from June 4 to 9, 1999. These proceedings (θ − θ)u = sin( ), (θ + θ)v = sin( ). comprise four sets of introductory lectures, and some thirty c 2 βc 2 (4) five papers of a more specialized nature. The introductory This over-determined system, which is known as the lectures are well written, and cover much of the founda- Backlund¨ transformation of the sine-Gordon equation, is lo- tional material at a level which will be accessible to non- cally solvable since the Frobenius integrability conditions experts. The specialized articles deal with a number of inter- are satisfied by virtue of the sine-Gordon equation (1). esting current trends in the geometrical and analytical study Backlund’s¨ theorem asserts that given a solution θ(u, v) of of certain special classes of differential equations by means the Backlund¨ transformation (4), the map X : U  ⊂ R2 → of Backlund¨ and Darboux transformations. Nearly all these R3 :(u, v) → X(u, v) defined by articles have been written with great care and attention to de- tail. Unlike many conference proceedings, this volume will    L θ − θ θ + θ likely become a useful reference in an active area of math- X = X + sin( )Xu +sin( )Xv , (5) sin θ 2 2 ematics which involves a rich mixture of classical differen- tial geometry, complex analysis, scattering theory, and Lie where ζ groups. L = c sin ζ, β = tan , (6) A review of the detailed contents of this book would be 2 nearly impossible given the breadth of the topics that it cov- gives rise to a pseudo-spherical surface S of constant nega-  1 ers. We have chosen instead to illustrate a number of the tive Gaussian curvature K = K = − c2 . The tangent planes main themes of the book on a classical example which car- at the corresponding points X(u, v) and X(u, v) make a ries at an elementary level many of the features of the general constant angle ζ.TheBacklund¨ transformation (4) can thus situation. be thought of as a technique for generating new solutions of The transformations that are nowadays referred to as the sine-Gordon equation from known ones by the integration Backlund¨ transformations have their origin in the classical in- of a compatible first-order quasi-linear system. One particu- vestigations of Lie, Backlund¨ and Bianchi on transformations larly nice feature of the Backlund¨ transformations (4) is that

14 NOTES de la SMC SEPTEMBER/SEPTEMBRE their composition is commutative with respect to the param- which exploit the invariance of the sine-Gordon equation un- eter β. This is known as the Bianchi Permutability Theorem. der Lorentz transformations of the (u, v)-plane viewed as the The sine-Gordon equation (1) is a non-linear hyperbolic Minkowski plane in null coordinates, equation, and it is quite remarkable that it admits closed-form 2 solutions which describe the interaction of solitary waves. ds = du dv. (12) These solutions are called soliton solutions. For example the solution given by In these variables, the identity component of the Lorentz group acts on the Minkowski plane by scaling, 1 1 θ = 4 arctan [ exp( (β +β−1)x+ (β −β−1)y)], (7) v 2c 2βc (u, v) → (au, ),a=0 , (13) a where and one may seek Lorentz-invariant solutions in the form x = u + v, y = u − v, (8) is the 1-soliton solution of the sine-Gordon equation. The θ(u, v)=g(z),z:= uv. (14) corresponding pseudo-spherical surface is known as a Dini After substituting the above in the sine-Gordon equation and surface, and is parametrized by X(x,y), given by letting sin ζ y sin ζ y w(z) = exp(ig), (15) [c cos( ),c sin( ),x− c sin ζ tanh χ] (9) cosh χ c cosh χ c we see that the Lorentz-invariant solutions are governed by the ordinary differential equation where x − y cos ζ  2  χ := . (10)  (w ) 2 w − w +1 c sin ζ w = + . (16) w 2 z The N-soliton solutions of the sine-Gordon equation are ob- tained by applying the Backlund¨ transformation (4) to the This is a special case of the equation defining the third of the 1-soliton solution and exploiting the Bianchi Permutability six Painleve´ transcendents. Theorem. These multi-soliton solutions describe the non- The last important property of the sine-Gordon equation linear interaction of traveling waves, which retain their ve- that we will briefly mention here is the existence of an infinite locity and shape after their interaction, but with a phase shift. family of conservation laws of arbitrary differential order, The parameter β which appears in the Backlund¨ transforma- giving rise to functionals which are commuting with respect tion plays the role of the spectral parameter in the solution of to a natural Poisson bracket. This fact bears a strong analogy the sine-Gordon equation by the method of inverse scatter- to the defining of completely integrable finite-dimensional ing, through a Lax pair formulation. Hamiltonian systems. The sine-Gordon equation is related in a very interesting The existence of multi-soliton solutions, of a Backlund¨ way to a certain ordinary differential equation of Painleve´ transformation involving a spectral parameter, of symme- type. Recall that a second-order ordinary differential equa- try reductions to ordinary differential equations of Painleve´ tions in the complex domain type and of an infinite hierarchy of commuting flows is often viewed as a meta-definition of the class of ”completely in- w = F (z,w,w), (11) tegrable” non-linear partial differential equations. The sine- Gordon is only one of a large number of equations which are is said to be of Painleve´ type if its solutions have no singu- completely integrable in this sense. Completely integrable larities depending on the initial conditions other than poles. equations are nevertheless very special, and the volume under Painleve´ showed that up to a natural group of transforma- review does a wonderful job of revealing their phenomenol- tions, there are fifty parametrized families of differential ogy, particularly through the prism of classical differential equations whose solutions enjoy this property. Six of these geometry. Still, one of the main open challenges in this sub- families are such that for generic values of their parame- ject is to fully understand why there are so few genuine ex- ters, the corresponding solutions define new transcendental amples known of ”completely integrable” non-linear partial functions, called the Painleve´ transcendents. The third of differential equations when the number of independent vari- these Painleve´ transcendents arises when one seeks solutions ables is higher than two.

15 SEPTEMBER/SEPTEMBRE CMS NOTES

NEWS FROM THE INSTITUTES

cations in numerical analysis, complex analysis and operator algebras. Summarizing, he said “this list shows that any- one who thinks he can work in one small corner is missing something–we’re all part of the same enterprise”. Other speakers were Angus Macintyre (Edinburgh), on Frobenius maps in model theory; Chris Rogers (Bath), Monte Carlo valuation of American options; Stephen Cook (Toronto), Propositional proofs of combinatorial principles; Vaughan Jones (Berkeley), Hilbert space representations of Temperley-Lieb algebras; and Karl Rubin (Stanford), Ranks of elliptic curves. At the banquet we were entertained by William Pulley- blank, formerly of Waterloo and now directing IBM’s Com- puting Institute. His subject was the computer simulation of protein folding. He explained that a protein is simply a chain of amino acids; there are only 20 of these acids and the chains can have up to 300 links. In water these chains assume com- plicated three-dimensional shapes, and the function depends on the configuration. The goal (“protein folding”) is a sys- tematic survey of the possibilities, with a view to designing proteins for specific tasks. For this one needs 1 petaflop per year of computing power; at present the 500 largest machines 10th Anniversary of the Fields Institute together can do only one-tenth of this. IBM is buiding a one- third petaflop parallel machine with 64,000 processors, due Justifiable pride was on display at the Fields Institute in June, in 2004. He concluded by pointing out the rapid emergence when its 10th anniversary was marked with a two-day event of the computer as a mathematical science tool, and with a that included lectures, a banquet and archival displays. There prediction that “designer drugs”, taking into account individ- was also a beautifully-produced 24 page booklet with brief ual genetic characteristics, will be here in four years. articles on many aspects of the Institute’s history and opera- For this reporter, who was involved over the past 15 years tions. In addition the honorary title of “Fields Institute Fel- in several aspects of the the Institute’s birth and operation, low” was created and conferred on 33 individuals for “out- this was a wonderful event: the beautiful building, the great standing contributions to the Institute, its programs, and to people, and above all the stimulating mathematics, combined the Canadian mathematical community” (see page 11 for memorably. Ken Davidson and his staff are to be congratu- more information about this). lated. The speakers, all of whom were involved in past events at the Institute, were led off by Martin Golubitsky (Hous- —Peter Fillmore ton), who described his work on modelling animal gaits. He recalled Leland Stanford’s early question: is there a point at NZ Institute Of Mathematics And Its Applications which all four of a galloping horse’s feet are off the ground? On 6 March 2002 the New Zealand government announced This led to the collection of data on an astonishing number of the formation of the New Zealand Institute of Mathematics gaits: walk, trot, pace, canter, gallop (transverse and rotary), and its Applications (NZIMA) as a Centre of Research Ex- and pronk. Fascinating bits of biology were mentioned, for cellence. Another new Center, the Allan Wilson Centre for example that dogs trot but cannot be made to pace. A simple Molecular Ecology and Evolution, has a major biomathemat- neurological model was described that can produce most of ics component. The establishment of these two research cen- these gaits by appropriate patterns of neuron firing. tres amounts to a revolution in mathematics research funding Persi Diaconis (Stanford) gave a masterful talk on pat- in New Zealand. terns in eigenvalues, typically via Haar measure on the uni- The NZIMA is based a the University of Auckland and tary group. The importance of this first came to light in statis- headed by Fields Medallist Vaughan Jones DSc FRS FRSNZ tics (data mining, Google), then physics (scattering, dynam- (Berkeley) and Professor Marston Conder (Auckland). It ical systems) and combinatorics (Ulam’s problem). He de- will be modelled on similar well-funded mathematical re- scribed in some detail a connection with the distribution of search institutes, notably the Fields Institute (Canada), IMPA the zeros of the zeta function, and mentioned further appli- (Brazil), MSRI (Berkeley), and the Newton Institute (UK).

16 NOTES de la SMC SEPTEMBER/SEPTEMBRE

In particular, it will place considerable emphasis on world- mation obtained with these new techniques. The Centre’s class research and the use of high-level mathematical tech- vision is to utilise the network of outstanding New Zealand niques in modern application areas such as bioengineering, biologists and mathematicians, who have made significant bioinformatics, medical statistics, operations research, and contributions to developing new analytical methods and tech- risk assessment. niques in this area, to address some of the fundamental ques- Its activities will include: tions about New Zealand’s plant and animal life. – the organization of two 6-month programmes each year, –Rod Downey, President of the NZ Mathematical Society on themes drawn from a range of fields of significant interest – an associated workshop held at various locations around New Zealand, like the New Zealand Mathematics Re- BIRS Proposals for 2004 search Institute Workshops held annually since 1995. – establishment of annual Maclaurin Fellowships, to en- The Banff International Research Station for Mathemat- able mathematical scientists from NZ or worldwide to take ical Innovation and Discovery (BIRS) is now accepting pro- time out from their usual occupations and undertake full-time posals for 2004. Full information, guidelines, and online research in New Zealand (or partly overseas if based in New forms are available at the website Zealand). http://pims.math.ca/birs It is expected that NZIMA will open for business later BIRS will be operating for 40 weeks in 2004 and will be this year. running either a full workshop (40 people for 5 days) or two The Allan Wilson Centre for Molecular Ecology and half-workshops (20 people for 5 days) each week. As usual, Evolution will be located at Massey University and directed BIRS provides full meals, accommodation, and research fa- by Professors David Penny (biology) and Michael Hendy cilities at no cost to the organizers and to the invited partici- (mathematics). It will undertake studies of the ecology pants. and evolution of New Zealand plants, animals and micro- In addition BIRS will operate its Research in Teams and organisms. Recent research, using new techniques such as Focused Research Groups programs, which allow smaller sequencing of whole genomes and the study of ancient DNA, groups of researchers to get together for several weeks of un- has revolutionized our understanding of New Zealand’s bio- interrupted work in a setting conducive to research and col- diversity. The simplistic view that New Zealand is a ’Moa’s laboration. Ark’ of relic species undergoing ’ancient and slow’ changes The deadline for BIRS workshop proposals is October over long periods of time has been overturned by the infor- 15, 2002.

CARLETON UNIVERSITY– OTTAWA, ONTARIO SCHOOL OF MATHEMATICS AND STATISTICS

Position in Mathematics and Statistics The School of Mathematics and Statistics invites applications for one or more tenure track positions at the rank of Assistant Professor and possibly higher starting July 1, 2003. Applicants should have a Ph.D. (by the time of appointment) in Mathemat- ics, Statistics, or related areas, a demonstrated potential for research and a strong commitment to excellence in teaching. The School is particularly interested in candidates who are actively engaged in research in applied areas of mathematics or statistics; however outstanding candidates in all areas of mathematics or statistics will be considered. More information about the School can be found at www.math.carleton.ca . These positions are subject to budgetary approval. Applications including a curriculum vitae and three letters of reference, should be sent to: Dr. C.W.L. Garner, Director School of Mathematics and Statistics Carleton University 1125 Colonel By Drive Ottawa, Ontario, K1S 5B6

Deadline for applications is October 1, 2002 but applications received after this date may be considered.

All qualified candidates are encouraged to apply. The applications of Canadians and Permanent Residents will be given priority. Carleton University is committed to equality of employment for women, aboriginal peoples, visible minorities, and persons with disabilities. Persons from these groups are encouraged to apply.

17 SEPTEMBER/SEPTEMBRE CMS NOTES

A Grad Student at the Laval Meeting by Tara Taylor, Dalhousie University

The annual CMS summer meeting was held this past June someone answers you back in English. So at the end of the 15-17 in Quebec´ City, at Laval University. I am currently evening, when I called for a taxi, I was thrilled to be answered a doctoral student at Dalhousie University, and this was my in French. first time as a participant at a CMS meeting. I was in Quebec´ Sunday began with a talk by Isadore Singer, “Forty Years only on Saturday and Sunday, so I was unable to participate Of Index Theory”. This was another talk where the math- in the entire meeting. It was all a bit overwhelming, there ematics went over my head, but I felt reassured when the were so many interesting things going on. I found that the speaker described how a talk should be broken down. The meeting was extremely well-organized, and there were many first five minutes should be understandable to your landlord, enthusiastic people around to answer all sorts of queries. and the next five minutes to an undergraduate math student, My experience began Saturday afternoon. I had been at- and so on with increasing complexity until the last five min- tending another mathematics conference in Michigan, and utes, which shouldn’t be understandable even to the speaker unfortunately I was delayed and had to miss the delegate’s himself. Then I participated in the “Experiencing Geome- luncheon. I did get to fly on a small propeller plane, which try Workshop” by David Henderson and Daina Taimina, that was quite a thrill. I must say that I was happy to be back in was part of the Math Education session. I found this work- Canada. I have only been to Quebec´ once before, so I was shop extremely enlightening and fun. We endeavoured to very excited to be there. I was not able to explore the city define “What is a straight line?” first on a plane, then on a as I was too busy at the meeting, and the weather was not sphere, a cone and finally on a hyperbolic plane. This was very agreeable anyways. Many people told me that Friday definitely a hands-on experience. Following the workshop, had been a glorious day and they were able to enjoy the city. I attended a talk where the slides were in English and the Oh well, a` la prochaine. So, with Dunkin’ Donuts for sus- speaker (Dominic Rochon) spoke French. I think this was tenance, I attended talks from a few different sessions. As an innovative way to bring both worlds together. Throughout a graduate student, I am just starting to focus on a specific the meeting it was truly wonderful to witness mathematics in topic. However, there are so many different areas of mathe- both languages. I attended various sessions throughout the matics that interest me, and so I often found it rather difficult afternoon, leaving my mind buzzing. to choose one talk to attend over many other equally appeal- ing ones. I am learning that it is okay to not understand ev- The Banquet took place Sunday evening at le Musee´ du erything in a talk. I can always glean something new, and it Quebec.´ This was certainly another highlight of the meeting. is always nice to meet other mathematicians from across the There were a few speeches, and I wasn’t quite able to under- country. stand everything, but I believe they were quite humourous. I Saturday evening I went to the Graduate Student Social at find that being a mathematician can often make one feel iso- Le Tapis Vert, and it was quite pleasant. One of the highlights lated, but at the banquet, and indeed thoughout the meeting, of the meeting was being able to hear and speak French. It the opposite was true. It was a joy to be part of a community. had been quite a long time since I had had the opportunity. I look forward to attending many more CMS meetings in the You know that you are not speaking French too well when years to come.

Letters to the Editors/Lettres aux Redacteurs´ The Editors of the Notes welcome letters in En- Les redacteurs´ des Notes acceptent les lettres en glish or French on any subject of mathematical franc¸ais ou en anglais portant sur un sujet d’inter´ etˆ interest but reserve the right to condense them. mathematique,´ mais ils se reservent´ le droit de Those accepted for publication will appear in the les comprimer. Les lettres acceptees´ paraˆıtront language of submission. Readers may reach us at dans la langue dans laquelle elles nous sont par- [email protected] or at the CMS Execu- venues. Les lecteurs pourront nous joindre au bu- tive Office. reau administratif de la SMC ou a` l’adresse suiv- ante: [email protected].

18 NOTES de la SMC SEPTEMBER/SEPTEMBRE

CMS Winter Meeting 2002 Financial Mathematics Ottawa Marriott Hotel (Org: Luis Seco, University of Toronto) Ottawa, Ontario Robert Almgren (Toronto), Abel Cadenillas (Alberta), Tahir December 8-10, 2002 Choulli (Alberta), Matt Davison (UWO), Tom Hurd (Mc- Master), Ali Lavassani (Calgary), Eric Renault (Montreal),´ First Announcement Tom Salisbury (York), Dave Saunders (Pittsburgh), Agnes Tourin (McMaster). Tony Ware (Calgary). On behalf of the University of Ottawa, the Department of Mathematics and Statistics invites all researchers, educators Finite Elements and students to the Winter 2002 Meeting of the Canadian (Org: Roger Pierre, Laval University) Mathematical Society (CMS). The Department is pleased to once again welcome col- Francois Bertrand (Ecole´ Polytechnique de Montreal),´ Yves leagues back to the Nation’s Capital. Following the usual for- Bourgault (Ottawa), Alain Charbonneau (UQAH), Kokou mat, the meeting will include twelve symposia, contributed Dossou (ICIP, Hull), Mohammed Farhloul (Moncton), Peter papers, four plenary speakers, as well as the Coxeter-James A. Forsyth (Waterloo), Andre´ Fortin (GIREF, Laval), Robert and Doctoral Prize lecturers and the awarding of the 2002 Guenette (GIREF, Laval), P.D. Minev (Alberta), Dominique Adrien Pouliot Prize. There will also be a Public Lecture Pelletier (Ecole´ Polytechnique de Montreal),´ Leila Slimane delivered by Robert Zuccherato of Entrust. (GIREF, Laval), Azzedine Soulaimani (Ecole´ de technologie All pre-meeting activities and scientific talks will be held superieure).´ at Ottawa Marriott Hotel, 100 Kent Street, steps away from Parliament Hill and Ottawa’s downtown core. History of Mathematics The most up-to-date information concerning the pro- (Org: Richard O’Lander and Ronald Sklar, grammes, including detailed schedules, will be made avail- St. Johns University N.Y.) able at the following web site: http://www.cms.math.ca/Events/winter02 Michael Barr (McGill), Jonathan Borwein (Simon Fraser), Meeting registration forms and hotel accommodation forms Florin Diacu (Victoria), Hardy Grant (Carleton), Francois are published in the September 2002 issue of the CMS Notes Major (Montreal), Michael Makkai (McGill), John McKay and are also available on the web site, along with on-line (Concordia), Angelo Mingarelli (Carleton), Gregory Moore forms for registration and submission of abstracts. (McMaster), Christiane Rousseau (Montreal),´ Luis Seco (Toronto), Walter Whiteley (York), Peter Zvengrowski (Cal- Public Lecture gary). Robert Zuccherato (Entrust) Lie Algebras and Moonshine (Org: Abdellah Sebbar and Erhard Neher, Plenary Speakers University of Ottawa) James Arthur (University of Toronto) Rene Carmona (Princeton University) Bruce Allison (Alberta), Yuri Bahturin (Memorial), Geor- Victor Guillemin (MIT) gia Benkart (Wisconsin-Madison), Nantel Bergeron (York), Maciej Zworski (Berkeley University) Stephen Berman (Saskatchewan), Yuly Billig (Carleton), Chris Cummins (Concordia), Drajomir Djokovic (Water- Prizes and Awards loo), Chongying Dong (California-Santa Cruz) Terry Gan- The CMS Coxeter-James Lecture will be given by Lisa non (Alberta), Yun Gao (York), Haisheng Li (Rutgers), John Jeffrey, University of Toronto. McKay (Concordia), Adrian Ocneanu (Pennsylvania State), The Doctoral Prize and the Adrien Pouliot Prize will also Arturo Pianzola (Alberta), Yoji Yoshii (Wisconsin-Madison), be awarded during this meeting. Noriko Yui (Queen’s).

Symposia Mathematical Education : Now I See !!!! By invitation of the Meeting Committee, there will be sym- Dynamic Visualisations in posia in the following areas. Here is the preliminary list of Canadian Mathematics Education speakers. If you are interested in being an invited speaker in (Org: Thomas Steinke, OCCDSB) one of the symposia, it may be possible to do so by contacting one of the organizers of that symposium. Keynote Speaker: Walter Whiteley (York). 19 SEPTEMBER/SEPTEMBRE CMS NOTES

Number Theory Symplectic Geometry (Org: Damien Roy, University of Ottawa, (Org: Lisa Jeffrey and Eckard Meinrenken, and Kenneth Williams, Carleton University) University of Toronto)

Peter Borwein (Simon Fraser), Douglas C. Bowman (Illinois Anton Alekseev (Geneva), Henrique Bursztyn (Toronto), Re- - Urbana-Champaign), Kwok-Kwong Stephen Choi (Simon becca Goldin (George Mason), Megumi Harada (California- Fraser), Henri Darmon (McGill), Chantal David (Concor- Berkeley), Tara Holm (MIT), Yael Karshon (Toronto), Ely dia), John Friedlander (Toronto), Eyal Goren (McGill), Man- Kerman (Toronto), Askold Khovanskii (Toronto), Misha Ko- fred Kolster (McMaster), Greg Martin (British Columbia), gan (Northeastern), Francois Lalonde (Quebec-Montr´ eal),´ David McKinnon (Waterloo), Yiannis Petridis (City Univ. Eugene Lerman (Illinois-Urbana-Champaign), David Met- of New-York), Cameron L. Stewart (Waterloo), Jeffrey Lin zler (Florida), Jonathan Weitsman (California-Santa Cruz), Thunder (Northern Illinois), Michel Waldschmidt (Paris VI). Siye Wu (Colorado-Boulder), Ping Xu (Pennsylvania State), Operator Algebras Carmen Young (Fields Institute), Catalin Zara (Yale). (Org: Thierry Giordano, and David Handelman, University of Ottawa) Theory and Applications of Point Processes (Org: Gail Ivanoff and David McDonald, Berndt Brenken (Calgary), Ken Davidson (Fields/Toronto), University of Ottawa) Man Duen Choi (Toronto), George Elliott (Toronto), Nigel Higson (Penn State), Mahmood Khoshkam (Saskatchewan), Francois Baccelli (Ecole´ Normale Superieure),´ Raluca Balan Claus Koestler (Queen’s), Dan Kucerovsky (UNB), Marcelo (Sherbrooke), Gail Ivanoff (Ottawa), Reg Kulperger (West- Laca (Victoria), Jamie Mingo (Queen’s), Vladimir Pestov ern Ontario), David McDonald (Ottawa), Richard Serfozo (Ottawa), John Phillips (Victoria), Ian Putnam (Victoria), (Georgia Institute of Technology), Yiqiang Q. Zhao (Car- Roland Speicher (Queen’s). leton). Partial Differential Equations Contributed Papers Session (Org: Victor Ivrii and John Toth, University of Toronto) (Org: to be announced) Richard Beals (Yale), Jim Colliander (Toronto), An- drew Comech (North Carolina-Chapel Hill), Walter Craig Contributed papers of 15 minutes duration are invited. Ab- (McMaster), Alan Greenleaf (Rochester), Peter Greiner stracts for CMS contributed papers should be prepared as (Toronto), Victor Guillemin (MIT), Victor Ivrii (Toronto), specified below. To better assist organizers, please include Vojkan Jaksksic (McGill), Kate Okikiolu (California- the Primary (2000) AMS Classification. SanDiego), Chris Sogge (John’s Hopkins), Catherine Sulem For an abstract to be eligible, the abstract must be re- (Toronto), John Toth (McGill), Guenter Uhlmann (Wash- ceived before October 15, 2002. The abstract must be ac- ington), Andras Vasy (MIT), Jared Wunsch (SUNY-Stony companied by its contributor’s registration form and payment Brook), Steve Zelditch (John’s Hopkins), Maciej Zworski of the appropriate fees. (Berkeley). Travel Grants for Graduate Students “Real-World” Problems in Search of Solutions (Org: Andre´ Dabrowski, University of Ottawa) Limited funds are available to partially fund the travel and accommodation costs for graduate students. For more infor- Xiaoyi Bao (Ottawa), Mary Hefford (Health Canada), Donal mation, please contact the Meeting Committee at gradtravel- Hickey (Ottawa), Andre´ Longtin (Ottawa), Rejean Munger [email protected]. (Ottawa Hospital Research Institute - Eye institute), Michael Applicants must be bona fide graduate students, at a Rudnicki (Ottawa Hospital Research Institute). Canadian or other University. To apply for this funding, Representation Theory of Real and p-adic Groups please have a letter written by your Supervisor or depart- (Org: Jason Levy and Monica Nevins, mental Graduate Advisor, briefly answering the following: University of Ottawa) Name of Student, Area of study and level, How will the stu- dent benefit from the meeting? Will the student be speaking? Heather Betel (Toronto), Clifton Cunningham (Calgary), What support is available from local sources or grants, for Stephen DeBacker (Harvard), Julee Kim (Institute for this student? Advanced Study), Jason Levy (Ottawa), Fiona Mur- Please have this sent before November 1, 2002.This naghan (Toronto), Monica Nevins (Ottawa), Alfred Noel¨ letter may be emailed to [email protected]. Ap- (Massachusetts-Boston), Eric Sommers (Massachusetts- plicants will be notified early in November of the funding Amherst), Yuanli Zhang (Montreal).´ decision.

20 NOTES de la SMC SEPTEMBER/SEPTEMBRE

If successful, the student will receive a cheque for reim- Abstracts may be sent electronically, following instruc- bursement of expenses upon completion and submission of tions given below. Electronic submission of abstracts is pre- the standard Travel Expense Claim Form, along with appro- ferred. If this is not possible, abstracts may also be pre- priate original receipts. pared on the standard form available from the CMS Exec- utive Office, 577 King Edward, Suite 109, Ottawa, Ontario Social Events CANADA K1N 6N5. Speakers are asked to submit their abstracts as soon as A welcoming reception will be held Saturday, December 7, possible. The deadline for submission of abstracts has been from 7:00 to 9:00 p.m. in the Victoria North Ballroom of the set at October 15, 2002. The organizers appreciate the coop- Ottawa Marriott Hotel. eration of all the speakers in observing this important dead- A Public Lecture Reception will be held in connection line. with the talk by Robert Zuccherato (Entrust). More details will be posted on our web site as they become available. Electronic submission of abstracts: To submit your ab- The Delegates’ Luncheon will be held on Sunday, stract, please go to the forms section of the meeting web site: December 8, from 12:30 to 2:00 p.m. in the Victoria http://cms.math.ca/Events/winter02/forms.html. North/South Ballrooms of the Ottawa Marriott Hotel. A ticket to this luncheon is included in all registration fee cate- Alternatively, files including the session, speaker’s name, gories. affiliation, complete address, title of talk, and abstracts may A banquet will be held on Sunday, December 8, from be sent to 7:30 p.m. in the Victoria North/South Ballrooms of the Ot- [email protected] (speakers), or tawa Marriott Hotel, preceded by a cash bar at 6:30 p.m. [email protected] (contributed pa- Tickets to this event are available at $50.00 each. pers). Coffee and juice will be available during the scheduled Please make sure to include the session name in your sub- breaks. ject line. For contributed papers, to better assist organizers, A detailed schedule of all social and other events is avail- please include the 2000 AMS Subject Classification. able from the schedule page of the meeting web site. Important deadline for submission of all abstracts: Business Meetings October 15, 2002 The CMS will be holding business meetings during the course of the meeting. The CMS Executive Committee Meeting will meet on Registration Friday, December 6, from 6:00 to 10:00 p.m in the Sussex Salon of the Ottawa Marriott Hotel. The registration form will appear in the September 2002 is- The CMS Development Group Luncheon will be held sue of the CMS Notes and are also available from: from 11:00 a.m. to 1:00 p.m. on Saturday, December 7 in the Sussex Salon of the Ottawa Marriott Hotel. CMS Executive Office The CMS Board of Directors Meeting will be held from 577 King Edward, Suite 109, P.O. Box 450, Station A 1:30 to 6:30 p.m. on Saturday, December 7 in the Wellington Ottawa, Ontario CANADA K1N 6N5 Salon of the Ottawa Marriott Hotel. Tel: 613-562-5702 FAX: 613-565-1539 A detailed schedule of business meetings and other Email: [email protected] events is available from the schedule page of the meeting web site. Electronic pre-registration is available at http://www.cms.math.ca/Events/winter02/forms.html Exhibits Payment for preregistration may be made by cheque, or by VISA or MasterCard. Although registration fees are given Exhibits will be held in the Victoria Gallery of the Ottawa in Canadian dollars, delegates may send cheques in US dol- Marriott Hotel during specified hours during the conference. lars by contacting their financial institution for the current exchange rate. Submission of Abstracts Please note that payment must be RECEIVED IN OT- Abstracts for all talks will be published in the TAWA on or before November 1 in order to qualify for meeting programme and will also be available at reduced rates. In order for your payment to be processed http://cms.math.ca/Events/winter02/abs/. before the meeting, it should be received by November 30.

21 SEPTEMBER/SEPTEMBRE CMS NOTES

Before After Delegate’s Luncheon included Nov 1 Nov 1 reserved at the locations given below and will be held until the deadlines specified. Reservations not made by that date Plenary speakers/prize lecturers $ 0 $ 0 Session speakers 215 215 will be on a space available basis. Rates are per room, per Organizers 145 145 night and are quoted in Canadian dollars. Non-members 430 560 CMS/AMS/MAA members with grants 290 375 Ottawa Marriott Hotel CMS/AMS/MAA members without grants 145 190 100 Kent Street, Ottawa (Ontario) Canada K1P 5R7 One-day fee 195 255 Postdocs, retired 110 145 Check-in: 3:00 p.m.; Check-out: 1:00 p.m. Teachers (K-12, CEGEP), students, unemployed 55 70 Applicable taxes: GST (7%), Hotel tax (5%) Banquet (free for plenary/prize speakers) 50 50 Deadline: November 6, 2002 CMS = Canadian Mathematical Society Group Code: CMS Winter Meeting 2002 AMS = American Mathematical Society Phone: 613-238-1122 toll-free: 800-853-8463 MAA = Mathematical Association of America FAX: 613-783-4238 Why Preregister? email: [email protected] parking: $15.00 daily (self-parking), $20.00 daily (valet parking) Wondering whether to pre-register or wait until you arrive? Rates: $128, single/double occupancy Here are some advantages to pre-registering. (Children 19 yrs old and under sharing parents’ – many can take advantage of reduced fees until the early accommodation are complimentary.) registration deadline (see above) Travelodge Hotel by Parliament Hill – your name would appear on the list of participants on our 402 Queen Street, Ottawa (Ontario) Canada K1R 5A7 web site Check-in: 3:00 p.m.; Check-out: 12:00 noon – your Meeting Kit will be waiting for you at the reception Applicable taxes: GST (7%), Hotel tax (5%) on Saturday evening Deadline: November 6, 2002 – no waiting in line early Sunday morning to process your Group Code: Cdn Mathematical Society Phone: 613-236-1133 Toll-free: 1-800-578-7878 registration ! FAX: 613-236-2317 – banquet tickets are available now but may no longer be email: [email protected] parking: $9.00 daily (self-parking) available on site plus taxes (in and out privileges) For all these reasons, we encourage you to preregister, Rates: $89, Standard Room, single/double occupancy whether it be before or after the early registration deadline. If $105, Deluxe Rooms, single/double occupancy you’d like to preregister and enjoy the above benefits, please $15 additional where a cot may be required visit our web site to use our online forms. (Children 17 yrs old and under sharing parents’ accommodation are complimentary.) Refund Policy In all cases, delegates must make their own reservations. The conference rate is extended up to two days pre- and post- Delegates wishing to cancel their registration must notify the convention. Where applicable, and in order for your room to CMS Executive Office in writing before November 30 to be applied against our block, please quote the group code. receive a refund less a $40 processing fee. Those whose con- tributed paper has not been accepted will upon request be Accommodation reservations and cancellations: For the fully refunded. Ottawa Marriott Hotel, all reservations must be guaranteed by a first night deposit, or major credit card guarantee. De- posit is refundable without penalty if an individual guest can- Do you qualify for free CMS cels a room reservation by 6:00 p.m. on the day of arrival. In membership? the case of a “no show” or if the guaranteed reservation not be cancelled by 6:00 p.m. on the day of arrival, the cost of An AMS or a MAA member who registers at a semi-annual the room for the first night will be charged to the guarantor. meeting of the CMS and who is not a member of the CMS, For the Travelodge Hotel by Parliament Hill, reserva- is eligible for a one-time only, one-year free membership in tions will be held until 6:00 p.m. on the day of arrival unless the CMS. guaranteed by a first night deposit, or major credit card guar- If you qualify, please visit the CMS booth to complete a antee. Should a guaranteed reservation not be cancelled by membership application form. Please provide proof of cur- 6:00 p.m. on the day of arrival, the cost of the room for the rent AMS or MAA membership. This offer applies to new first night will be charged to the guarantor. members only. Accommodation Child Care It is recommended that those attending the conference book The following information was provided by the meeting ho- early to avoid disappointment. Blocks of rooms have been tels. Advance research and arrangements are recommended.

22 NOTES de la SMC SEPTEMBER/SEPTEMBRE

The Ottawa Marriott Hotel offers onsite a fully equipped Acknowledgements unsupervised “Children’s Activity Centre”, complete with Support from the following is gratefully acknowledged: Playstations, a variety of toys and games for all ages. For - University of Ottawa, Department of Mathematics and individual child care, the hotel recommends Gigi’s Childcare Statistics 613-749-1295. - The National Programme Committee (a joint funding body The Travelodge Hotel by Parliament Hill will also pro- of the Centre de recherches mathematiques,´ The Fields Insti- vide recommendations. Please contact the hotel directly to tute for Research in Mathematical Sciences, and The Pacific make enquiries. Institute for the Mathematical Sciences) Updates will be posted to the meeting web site as they become available. The Canadian Mathematical Society would like to acknowl- Travel edge the contribution of the members of the Meeting Com- mittee for organizing this meeting. The City of Ottawa: The Nation’s Capital has much to ex- plore during winter or summer. The festival of lights on Par- Meeting Committee liament Hill is a must-see for anyone visiting in December. We hope you’ll take the opportunity to bring your family, Programme explore the city and take in some great attractions and shop- Meeting Director: Daniel Daigle (Ottawa) ping. Andre´ Dabrowski (Ottawa), Thierry Giordano (Ottawa), Detailed information regarding the University of Ottawa David Handelman (Ottawa), Gail Ivanoff (Ottawa), Vic- and the city of Ottawa, including tourism information, local tor Ivrii (Toronto), Lisa Jeffrey (Toronto), Jason Levy weather and climate, car rental information, site and street (Ottawa), David McDonald (Ottawa), Eckard Meinrenken maps, and suggested One Day Itineraries for self-guided (Toronto), Erhard Neher (Ottawa), Monica Nevins (Ottawa), tours, are available at the following web sites: Richard O’Lander (St. Johns N.Y.), Roger Pierre (Laval), http://www.uottawa.ca/ Damien Roy (Ottawa), Abdellah Sebbar (Ottawa), Luis Seco http://www.ottawa-conventions.com/ (Toronto), Ronald Sklar (St. Johns N.Y.), Thomas Steinke http://weatheroffice.ec.gc.ca/canada e.html (OCCDSB), John Toth (Toronto), Kenneth Williams (Car- leton), Graham Wright (CMS ex-officio). Parking: Guests at the Ottawa Marriott Hotel may park for a daily fee of $15.00 for self-parking or $20.00 for valet park- Local Arrangements ing, both including full in-and-out privileges. Chairs: Walter D. Burgess (Ottawa) and Andre´ Dabrowski Guests at the Travelodge Hotel by Parliament Hill may (Ottawa) park for a daily fee of $9.00, including full in-and-out privi- Monique Bouchard (CMS ex-officio). leges.

CMS MEMBERSHIP ADHESION´ ALASMC` The 2003 Membership Notices have Les avis d’adhesion´ 2003 ont et´ e´ been mailed. Please renew your postes.´ Veuillez renouveller votre membership now. To renew elec- adhesion´ maintenant. Vous pou- tronically, please visit our website at vez aussi renouveller au site web www.cms.math.ca www.smc.math.ca

23 SEPTEMBER/SEPTEMBRE CMS NOTES

Reunion´ d’hiver de la SMC Symposiums Hotelˆ Marriott Ottawa Le Comite´ de coordination a organise´ des symposiums sur les themes` qui suivent. Voici la liste preliminaire´ des Ottawa (Ontario) conferenciers.´ Si on est interess´ e´ a` faire un expose´ comme 8-10 decembre´ 2002 conferencier´ invite´ dans l’un des symposiums, on peut en faire la demande aupres` des organisateurs de ce symposium. Premiere` annonce Mathematiques´ financieres` (Org: Luis Seco, Universite´ de Toronto) Au nom de l’Universite´ d’Ottawa, le Departement´ de mathematiques´ et de statistique souhaite cordialement la Robert Almgren (Toronto), Abel Cadenillas (Alberta), Tahir bienvenue a` tous les participants alaR` eunion´ d’hiver 2002 Choulli (Alberta), Matt Davison (UWO), Tom Hurd (Mc- de la Societ´ emath´ ematique´ du Canada (SMC). Master), Ali Lavassani (Calgary), Eric Renault (Montreal),´ Les membres du departement´ sont heureux de recevoir Tom Salisbury (York), Dave Saunders (Pittsburgh), Agnes encore une fois les participants dans la capitale nationale. Tourin (McMaster). Tony Ware (Calgary). Conformement´ au format habituel, la Reunion´ compren- dra douze symposiums, des communications libres, qua- El´ ements´ finis tre conferences´ principales ainsi que les conferences´ des (Org: Roger Pierre,UniversiteLaval)´ laureats´ des prix Coxeter-James et de Doctorat. De plus, le prix Adrien-Pouliot sera decern´ e´ pendant la reunion´ et une Francois Bertrand (Ecole´ Polytechnique de Montreal),´ Yves conference´ populaire sera donnee´ par Robert Zuccherato de Bourgault (Ottawa), Alain Charbonneau (UQAH), Kokou Entrust. Dossou (ICIP, Hull), Mohammed Farhloul (Moncton), Peter Toutes les activites´ au programme et celles qui prec´ edent` A. Forsyth (Waterloo), Andre´ Fortin (GIREF, Laval), Robert la Reunion´ se derouleront´ al’H` otelˆ Marriott Ottawa (100, Guenette (GIREF, Laval), P.D. Minev (Alberta), Dominique rue Kent) situe´ au centre-ville a` quelques pas de la Colline Pelletier (Ecole´ Polytechnique de Montreal),´ Leila Slimane du Parlement. (GIREF, Laval), Azzedine Soulaimani (Ecole´ de technologie Vous trouverez l’information la plus recente´ sur les pro- superieure).´ grammes, y compris les horaires, a` l’adresse Web suivante : Histoire des mathematiques´ http://www.smc.math.ca/Reunions/hiver02/ (Org: Richard O’Lander et Ronald Sklar, Vous trouverez les formulaires d’inscription et de Universite´ St. Johns N.Y.) reservation´ d’hotelˆ dans le numero´ de septembre 2002 des Notes de la SMC. Ils seront aussi publies´ sur notre site Web, Michael Barr (McGill), Jonathan Borwein (Simon Fraser), tout comme les formulaires electroniques´ d’inscription et de Florin Diacu (Victoria), Hardy Grant (Carleton), Francois presentation´ des resum´ es.´ Major (Montreal), Michael Makkai (McGill), John McKay (Concordia), Angelo Mingarelli (Carleton), Gregory Moore (McMaster), Christiane Rousseau (Montreal),´ Luis Seco Conference´ populaire (Toronto), Walter Whiteley (York), Peter Zvengrowski (Cal- Robert Zuccherato (Entrust) gary).

Algebres` de Lie et Moonshine Conferenciers´ principaux (Org: Abdellah Sebbar et Erhard Neher, Universite´ d’Ottawa) James Arthur (Universite´ de Toronto) Rene Carmona (Universite´ Princeton) Bruce Allison (Alberta), Yuri Bahturin (Memorial), Geor- Victor Guillemin (MIT) gia Benkart (Wisconsin-Madison), Nantel Bergeron (York), Maciej Zworski (Universite´ Berkeley) Stephen Berman (Saskatchewan), Yuly Billig (Carleton), Chris Cummins (Concordia), Drajomir Djokovic (Water- Prix loo), Chongying Dong (California-Santa Cruz) Terry Gan- non (Alberta), Yun Gao (York), Haisheng Li (Rutgers), John La conference´ Coxeter-James de la SMC sera donnee´ par McKay (Concordia), Adrian Ocneanu (Pennsylvania State), Lisa Jeffrey, de l’Universite´ de Toronto. Arturo Pianzola (Alberta), Yoji Yoshii (Wisconsin-Madison), De plus, le Prix de Doctorat et le Prix Adrien-Pouliot Noriko Yui (Queen’s). seront decern´ es´ alaR` eunion.´ 24 NOTES de la SMC SEPTEMBER/SEPTEMBRE

Enseignement des mathematiques:´ Theorie´ des representations´ Maintenant je vois !!!! des groupes reels´ et p-adiques Visualisations dynamiques dans l’enseignement (Org: Jason Levy et Monica Nevins, Universite´ d’Ottawa) des mathematiques´ au Canada (Org: Thomas Steinke, OCCDSB) Heather Betel (Toronto), Clifton Cunningham (Calgary), Orateur principal: Walter Whiteley (York). Stephen DeBacker (Harvard), Julee Kim (Institute for Theorie´ des nombres Advanced Study), Jason Levy (Ottawa), Fiona Mur- (Org: Damien Roy,Universite´ d’Ottawa, naghan (Toronto), Monica Nevins (Ottawa), Alfred Noel¨ et Kenneth Williams,Universite´ Carleton) (Massachusetts-Boston), Eric Sommers (Massachusetts- Amherst), Yuanli Zhang (Montreal).´ Peter Borwein (Simon Fraser), Douglas C. Bowman (Illinois- Urbana-Champaign), Kwok-Kwong Stephen Choi (Simon Fraser), Henri Darmon (McGill), Chantal David (Concor- Geom´ etrie´ symplectique dia), John Friedlander (Toronto), Eyal Goren (McGill), Man- (Org: Lisa Jeffrey et Eckard Meinrenken, fred Kolster (McMaster), Greg Martin (British Columbia), Universite´ de Toronto) David McKinnon (Waterloo), Yiannis Petridis (City Univ. of New York), Cameron L. Stewart (Waterloo), Jeffrey Lin Thunder (Northern Illinois), Michel Waldschmidt (Paris VI). Anton Alekseev (Geneva), Henrique Bursztyn (Toronto), Re- Algebres` des operateurs´ becca Goldin (George Mason), Megumi Harada (California- (Org: Thierry Giordano,etDavid Handelman, Berkeley), Tara Holm (MIT), Yael Karshon (Toronto), Ely Universite´ d’Ottawa) Kerman (Toronto), Askold Khovanskii (Toronto), Misha Ko- gan (Northeastern), Francois Lalonde (Quebec-Montr´ eal),´ Berndt Brenken (Calgary), Ken Davidson (Fields/Toronto), Eugene Lerman (Illinois-Urbana-Champaign), David Met- Man Duen Choi (Toronto), George Elliott (Toronto), Nigel zler (Florida), Jonathan Weitsman (California-Santa Cruz), Higson (Penn State), Mahmood Khoshkam (Saskatchewan), Siye Wu (Colorado-Boulder), Ping Xu (Pennsylvania State), Claus Koestler (Queen’s), Dan Kucerovsky (UNB), Marcelo Carmen Young (Fields Institute), Catalin Zara (Yale). Laca (Victoria), Jamie Mingo (Queen’s), Vladimir Pestov (Ottawa), John Phillips (Victoria), Ian Putnam (Victoria), Roland Speicher (Queen’s). Theorie´ et applications des processus ponctuels Equations´ aux deriv´ ees´ partielles (Org: Gail Ivanoff et David McDonald, Universite´ d’Ottawa) (Org: Victor Ivrii et John Toth,Universite´ de Toronto)

Richard Beals (Yale), Jim Colliander (Toronto), An- drew Comech (North Carolina-Chapel Hill), Walter Craig Francois Baccelli (Ecole´ Normale Superieure),´ Raluca Balan (McMaster), Alan Greenleaf (Rochester), Peter Greiner (Sherbrooke), Gail Ivanoff (Ottawa), Reg Kulperger (West- (Toronto), Victor Guillemin (MIT), Victor Ivrii (Toronto), ern Ontario), David McDonald (Ottawa), Richard Serfozo Vojkan Jaksksic (McGill), Kate Okikiolu (California- (Georgia Institute of Technology), Yiqiang Q. Zhao (Car- SanDiego), Chris Sogge (John’s Hopkins), Catherine Sulem leton). (Toronto), John Toth (McGill), Guenter Uhlmann (Wash- ington), Andras Vasy (MIT), Jared Wunsch (SUNY-Stony Brook), Steve Zelditch (John’s Hopkins), Maciej Zworski Communications libres (Berkeley). (Org. : a` confirmer) Problemes` mathematiques´ provenant du monde industriel (Org: Andre´ Dabrowski, Universite´ d’Ottawa) Nous lanc¸ons un appel de communications libres de 15 mi- nutes chacune. Les resum´ es´ devront respecter les criteres` Xiaoyi Bao (Ottawa), Mary Hefford (Sante´ Canada), Donal precis´ es´ ci-dessous et nous parvenir au plus tard le 15 octo- Hickey (Ottawa), Andre´ Longtin (Ottawa), Rejean Munger bre 2002. Nous demandons a` chacun de joindre au resum´ ele´ (Institut de recherche de l’Hopitalˆ Ottawa - Institut de l’oeil), formulaire d’inscription et le reglement` des frais pertinents. Michael Rudnicki (Institut de recherche de l’Hopitalˆ Ot- Pour les communications libres, veuillez indiquer la classifi- tawa). cation de sujet AMS 2000.

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Subventions pour etudiants´ diplomˆ es´ Le lunch du Groupe de developpement´ de la SMC aura Les etudiants´ diplomˆ es´ ont acces` a` un fonds limite´ pour fi- lieude11ha13hlesamedi7d` ecembre´ au Salon Sussex de nancer une partie de leurs frais de deplacement´ et de sejour.´ l’Hotelˆ Marriott Ottawa. Pour de plus amples renseignements, veuillez communi- La reunion´ du Conseil d’administration de la SMC quer avec le Comite´ de coordination a` l’adresse suivante : aura lieu de 13 h 30 a` 18 h 30 le samedi 7 decembre´ au Salon [email protected]. Wellington de l’Hotelˆ Marriott Ottawa. Les demandeurs doivent etreˆ des etudiants´ de deuxieme` Un horaire detaill´ e´ des seances´ de travail et des autres ou de troisieme` cycle inscrits dans une universite´ canadi- ev´ enements´ est disponible a` la page des horaires du site Web. enne ou etrang´ ere.` Toute demande de financement doit etreˆ accompagnee´ d’une lettre du superviseur de l’etudiant´ ou Exposition de la personne responsable des etudes´ superieures´ de son Les kiosques d’exposition seront ouverts dans la Galerie Vic- departement,´ dans laquelle il ou elle indiquera le nom de toriadel’Hotelˆ Marriott Ottawa aux heures indiquees.´ l’etudiant,´ son domaine et son niveau d’etudes,´ en quoi la Reunion´ sera profitable al’` etudiant,´ si l’etudiant´ presentera´ une communication et si l’etudiant´ a acces` a` d’autres sources Envoi des resum´ es´ de financement de son universite´ (bourses, subventions, etc.). Tous les resum´ es´ paraˆıtront dans le programme de Cette lettre doit parvenir alaSMCavantle` la Reunion´ et seront accessibles sur le site Web : er 1 novembre2002 et peut etreˆ envoyee´ par courriel http://smc.math.ca/Reunions/hiver02/res/ ([email protected]). Les decisions´ seront an- Les participants peuvent envoyer leur resum´ e´ sous forme noncees´ au debut´ de novembre. electronique´ en suivant les instructions ci-dessous. Il est Si une subvention est accordee´ al’` etudiant,´ ce dernier pref´ erable´ de remettre les resum´ es´ par voie electronique,´ se verra rembourser ses depenses´ sur presentation´ du formu- mais si ce n’est pas possible, vous pouvez utiliser le formu- laire de remboursement approprie´ accompagne´ des rec¸us ori- laire standard que vous pourrez vous procurer au ginaux. Bureau administratif de la SMC, 577, avenue King-Edward, Activites´ sociales bureau 109, Ottawa (Ontario) Canada K1N 6N5. Les conferenciers´ sont pries´ de remettre leur resum´ ele´ Une reception´ aura lieu le samedi 7 decembre,´ de 19 h a21h,` plus totˆ possible. La date limite est fixee´ au 15 octobre a` la salle de bal Victoria Nord de l’Hotelˆ Marriott Ottawa. 2002. Les organisateurs remercient les conferenciers´ de bien Une reception´ pour la conference´ populaire aura lieu vouloir respecter cette importante ech´ eance.´ avant la conference´ de Robert Zuccherato (Entrust). Nous Envoi electronique´ des resum´ es´ : Pour en- publierons tout nouveau renseignement sur le site Web des` voyer votre resum´ e,´ rendez-vous alasection` que nous le recevrons. des formulaires du site Web de la Reunion´ : Le lunch des participants se tiendra le dimanche 8 http://smc.math.ca/Reunions/hiver02/forms.html decembre,´ de 12 h 30 a14h,` a` la salle de bal Victoria Nord/Sud de l’Hotelˆ Marriott Ottawa. Ce repas est compris Vous pouvez aussi nous faire parvenir par courriel dans toutes les categories´ d’inscription. un fichier comprenant le nom de la seance,´ le nom du Un banquet aura lieu le dimanche 8 decembre,´ a` compter conferencier,´ son affiliation, son adresse complete,` le titre de de 19 h 30, a` la salle de bal Victoria Nord/Sud de l’Hotelˆ la conference´ et le resum´ e´ a` l’une des adresses suivantes : [email protected] Marriott Ottawa. Il y aura un service de bar payant a` partir (conferenciers´ invites),´ [email protected] de 18 h 30 . On peut se procurer des billets pour cette activite´ ou (communications au coutˆ de 50 $ chacun. libres). Du cafe´ et des jus seront servis pendant les pauses. N’oubliez pas de preciser´ le nom de la seance´ dans le Un horaire detaill´ e´ de toutes les activites´ sociales et des sujet de votre message. Pour les communications libres, autres ev´ enements´ est disponible a` la page des horaires du veuillez indiquer la classification de sujet AMS 2000. site Web. Important – Date limite de remise des resum´ es´ : 15 octobre 2002. Seances´ de travail La SMC organisera des seances´ de travail a` l’occasion de Inscription cette Reunion.´ Un formulaire d’inscription paraˆıtra dans le numero´ de Le Comiteex´ ecutif´ de la SMC tiendra une reunion´ le septembre 2002 des Notes de la SMC. On peut egalement´ se vendredi 6 decembre´ de 18 h a` 22 h au Salon Sussex de le procurer aupres` de la SMC : l’Hotelˆ Marriott Ottawa.

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Bureau administratif de la SMC, 577, av. King-Edward, bureau 109 Politique de remboursement C.P. 450, Succursale A, Ottawa (Ontario) CANADA K1N 6N5 Les participants qui desirent´ annuler leur inscription doivent Tel´ ephone´ : 613-562-5702, Tel´ ecopieur´ : 613-565-1539 Courriel : [email protected] en aviser le bureau administratif de la SMC par ecrit´ avant le 30 novembre pour se voir rembourser leurs frais Vous pouvez aussi vous inscrire sur le Web au : d’inscription (moins 40 $). Les participants dont les commu- http://smc.math.ca/Reunions/hiver02/forms.html nications libres n’auront pas et´ e´ acceptees´ seront rembourses´ integralement´ sur demande. Les frais (en devises canadiennes) sont payables par cheque,` VISA ou MasterCard. Les paiements en devises americaines´ ˆ seront acceptes,´ mais nous vous demandons de contacter Etes-vous admissible a` une adhesion´ votre institution financiere` pour prendre connaissance du gratuite alaSMC?` taux de change en vigueur. Les membres de l’AMS et de la MAA qui s’inscrivent a` une Le paiement doit nous PARVENIR AOTTAWAauplus` er Reunion´ semestrielle de la SMC et qui ne sont pas membres tard le 1 novembre pour que vous ayez droit aux ta- de la SMC sont admissibles a` une annee´ d’adhesion´ gratuite rifs reduits.´ Pour que votre inscription soit traitee´ avant la a` la SMC (offre unique). Reunion,´ votre paiement doit nous parvenir au plus tard le 30 Si vous etesˆ admissible, presentez-vous´ au kiosque de la novembre. SMC pour remplir une demande d’adhesion.´ Veuillez fournir Avant le Apres` le er er Lunch des participants inclus 1 nov 1 nov une preuve d’adhesion´ al’AMSou` a` la MAA. Cette offre est destinee´ aux nouveaux membres seulement. Conferenciers´ principaux ou primes´ $0 $0 Conferenciers´ 215 215 Organisateurs 145 145 Hebergement´ Non-membres 430 560 Membres SMC/AMS/MAA avec subvention 290 375 Il est fortement recommande´ aux participants de reserver´ a` Membres SMC/AMS/MAA sans subvention 145 190 l’avance. Des chambres ont et´ e´ retenues aux endroits ci- Frais d’une journee´ 195 255 Postdocs, retraites´ 110 145 dessous jusqu’aux dates precis´ ees.´ Apres` ces dates, les hotelsˆ Enseignant(e)s (el´ em.,´ second., CEGEP),´ ne prendront vos reservations´ que s’il reste des chambres. etudiant(e)s,´ sans-emploi 55 70 Banquet (gratuits pour principaux/primes)´ 50 50 Les tarifs sont par nuit, par personne, et sont indiques´ en de- vises canadiennes. SMC = Societ´ e´ mathematique´ du Canada AMS = American Mathematical Society Hotelˆ Marriott Ottawa MAA = Mathematical Association of America 100, rue Kent, Ottawa (Ontario) Canada K1P 5R7 Arrivee´ : 15 h; depart´ : 13 h Taxes applicables : TPS (7 %), taxe d’hotelˆ (5 %) A` quoi sert de s’inscrire a` l’avance? Reserver´ au plus tard le 6 novembre 2002 Code de groupe : CMS Winter Meeting 2002 Tel´ ephone´ : 613-238-1122 sans frais : 800-853-8463 Vous vous demandez si vous devriez vous inscrire a` l’avance Tel´ ecopieur´ : 613-783-4238 ou le faire sur place? Voici quelques-uns des avantages de la courriel : [email protected] preinscription´ : stationnement : 15 $ la nuit, 20 $ avec service voiturier (entrees´ et – plusieurs personnes ont droit a` une reduction´ en sorties illimitees)´ s’inscrivant avant la date limite pour tarifs reduits´ (voir sec- Tarifs : 128 $, 1 ou 2 personnes tion ci-dessus) (Gratuit pour les enfants de moins de 20 ans qui partagent la chambre de leurs parents.) – votre nom figure dans la liste Web des participants sur le site Web Travelodge Hotel by Parliament Hill 402, rue Queen, Ottawa (Ontario) Canada K1R 5A7 – votre trousse d’inscription sera dej´ apr` eteˆ a` votre arrivee´ le Arrivee´ : 15 h; depart´ : 12 h samedi soir Taxes applicables : TPS (7 %), taxe d’hotelˆ (5 %) – vous n’aurez pas besoin de faire la file pour vous inscrire a` Reserver´ au plus tard le 6 novembre 2002 la premiere` heure dimanche matin Code de groupe : Cdn Mathematical Society – les billets pour le banquet sont en vente maintenant, mais il Tel´ ephone´ : 613-236-1133 sans frais: 800-578-7878 pourrait ne plus en rester sur place Tel´ ecopieur´ : 613-236-2317 courriel : [email protected] Pour ces raisons, nous vous encouragons a` vous incrire a` Stationnement: 9 $ la nuit + taxes (entrees´ et sorties illimitees)´ Tarifs : 89 $, standard, 1 ou 2 personnes ` ´ l’avance, soit avant ou apres la date limite pour tarifs reduits. 105 $, deluxe, 1 ou 2 personnes Pour vous inscrire a` l’avance et profiter des avantages ci- 15 $ additionnels si un lit pliant est requis dessus, rendez-vous sur notre site Web et remplissez les for- (gratuit pour les enfants de moins de 18 ans mulaires appropries´ . qui partagent la chambre de leurs parents) 27 SEPTEMBER/SEPTEMBRE CMS NOTES

Vous etesˆ pries´ de faire vos propres reservations.´ Les tarifs touristiques, temperature´ et climat locaux, cartes de la ville et pref´ erentiels´ s’appliquent aussi aux deux jours qui prec´ edent` des attractions touristiques, etc.) sur les sites Web suivants : et qui suivent la Reunion.´ S’il y a lieu et pour que votre cham- http://www.uottawa.ca/ bre soit prise dans le groupe de chambres reserv´ ees,´ veuillez http://www.ottawa-conventions.com/ donner le code de groupe. http://weatheroffice.ec.gc.ca/canada f.html Reservations´ et annulations : A` l’Hotelˆ Marriott Ot- tawa, pour chaque reservation,´ l’hotelˆ doit recevoir un dep´ otˆ Stationnement : Le stationnement al’H` otelˆ Marriott Ottawa equivalant´ alapremi` ere` nuit paye´ par cheque,` une carte de est disponible pour 15 $ la nuit, 20 $ avec service voiturier credit´ reconnue ou une lettre de garantie acceptable. Tout (entrees´ et sorties illimitees).´ dep´ otˆ est remboursable sans penalit´ e´ si une personne annule Au Travelodge by Parliament Hill, vous pouvez station- sa reservation´ avant 18 h la date d’arrivee.´ Autrement, le ner pour 9 $ la nuit (entrees´ et sorties illimitees).´ dep´ otˆ en entier ne sera pas rembourse.´ Si une personne ne se presente´ pas al’h` otel,ˆ on lui facturera la premiere` nuit de sa reservation.´ Remerciements Au Travelodge by Parliament Hill, les chambres sont Nous remercions les organismes suivants de leur soutien fi- reserv´ ees´ jusqu’a` 18 h le jour de l’arrivee,´ a` moins que la nancier : reservation´ ne soit garantie par le paiement d’une nuit ou par -leDepartement´ de mathematiques´ et de statisque de une carte de credit´ reconnue. Si une reservation´ garantie n’est l’Universite´ d’Ottawa pas annulee´ avant 18 h la date d’arrivee´ prevue,´ on facturera -leComite´ du programme national (programme conjoint du au client la premiere` nuit. Centre de recherches mathematique,´ de l’Institut Fields et de l’Institut Pacific) Services de garde Les renseignements suivants ont et´ e´ fournis par les hotelsˆ La Societ´ emath´ ematique´ du Canada tient a` remercier les prevus´ pour la Reunion.´ On vous recommande de faire vos membres du Comite´ de coordination pour l’organisation de demarches´ et vos reservations´ a` l’avance. cette Reunion.´ L’Hotelˆ Ottawa Marriott met a` la disposition de ses clients un centre d’activites´ pour enfants tout equip´ e´ (sans surveillance) comprenant des Playstations, des jouets et des Comite´ de coordination jeux pour toute la famille. Pour les services de garde indi- Programme viduels, l’hotelˆ recommande Gigi’s Childcare, au (613) 749- President´ et coordinateur : Daniel Daigle (Ottawa) 1295. Andre´ Dabrowski (Ottawa), Thierry Giordano (Ottawa), Le Travelodge Hotel by Parliament Hill peut aussi faire David Handelman (Ottawa), Gail Ivanoff (Ottawa), Vic- des recommandations au besoin. Priere` de communiquer tor Ivrii (Toronto), Lisa Jeffrey (Toronto), Jason Levy avec l’hotelˆ directement pour faire une demande. (Ottawa), David McDonald (Ottawa), Eckard Meinrenken Nous publierons tout nouveau renseignement sur le site (Toronto), Erhard Neher (Ottawa), Monica Nevins (Ottawa), Web des` que nous le recevrons. Richard O’Lander (St. Johns N.Y.), Roger Pierre (Laval), Damien Roy (Ottawa), Abdellah Sebbar (Ottawa), Luis Seco Deplacements´ (Toronto), Ronald Sklar (St. Johns N.Y.), Thomas Steinke Ville d’Ottawa : La capitale nationale a beaucoup aoffriren` (OCCDSB), John Toth (Toronto), Kenneth Williams (Car- hiver comme en et´ e.´ Le festival des lumieres` sur la Colline leton), Graham Wright (SMC, d’office). du Parlement est au nombre des ev´ enements´ de decembre´ a` ne pas manquer. Nous esperons´ que vous en profiterez pour Logistique amener votre famille, decouvrir´ la ville, magasiner et visiter Presidents´ du comite´ local : quelques-uns des plus beaux attraits de la capitale. Walter D. Burgess (Ottawa) et Andre´ Dabrowski (Ottawa) Vous trouverez des renseignements detaill´ es´ sur Monique Bouchard (SMC, d’office). l’Universite´ d’Ottawa et la ville d’Ottawa (renseignements

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31 SEPTEMBER/SEPTEMBRE CMS NOTES

From the President’s Desk by Christiane Rousseau

This is my first message to you as the President of the recipient of the Krieger-Nelson Prize, and Edwin Perkins, re- Canadian Mathematical Society. Over the past 57 years, cipient of the CMS Jeffery-Williams Prize. Quebec City’s thanks to the effort and commitment of hundreds of mem- French flavour permeated the congress, and some of us dis- bers of the Canadian mathematics community, the CMS has covered the pleasure of talking in French with our colleagues grown to become a major organization. What’s more, our from other provinces. In terms of plenary activities, two pre- discipline is in better health than it was just a few years ago. sentations were given in French, the public lecture by Jean- With three institutes and BIRS, our research infrastructure is Marie de Koninck and the plenary address by Robert Lang- now very well developed, and the scientific programs of these lands. At the banquet, Bernard Hodgson kept the audience institutions cover a broad spectrum of mathematical science. laughing in both English and French. A number of students We have strengthened our ties with industry and defended the attended the congress and presented papers. role of mathematics in all areas of strategic innovation, and Jonathan Borwein has now completed his term as Pres- we are now beginning to see our efforts bear fruit. Promot- ident of the CMS. On behalf of the Canadian Mathemati- ing our discipline to grant organizations is now easier than cal Society, it gives me great pleasure to thank him for the before. The activities that we have offered to the general wonderful things he has accomplished for the CMS, and for public in recent years-particularly during World Mathemati- all the work he did for the Canadian mathematics commu- cal Year 2000 have helped to burnish mathematics’ image in nity for so many years, particularly during his term as Pres- the eyes of the media and the public. We have forged new ident. Jonathan Borwein has made his mark in all areas of links with educational institutions and we look forward to the CMS’s activities: publications, electronic services, edu- playing a leadership role in mathematics education in this cation, research, and international affairs. Besides his out- country. standing work in all these areas, Jonathan Borwein has also We must remain vigilant, however, because there are still worked behind the scenes to make the CMS a better orga- clouds on the horizon. One concern is what is happening in nization: administrative management, office location prob- scientific publications. Our publications revenues fund many lems, fundraising to balance budgets, etc. In all these areas, of our other activities. If the publications market collapses, the CMS has profited from his broad perspective on problems we will have to cut budgets for educational programs, elec- and his unstinting efforts to solve them. tronic services and research activities. Another concern is the Now we are starting a new year. Here are some of our up- number of members of our community who will soon be re- coming activities. This will be the first year for the ”NSERC- tiring; we must recruit young people at Canadian universities CMS Math in Moscow” program. On May 16-18, 2003 the as new CMS members and convince them to work with us. National Educational Forum will be held at UQAM in Mon- Over the next few years, the CMS will continue to serve the treal. The Winter Meeting 2002 will take place in Ottawa and Canadian mathematics community and to promote our disci- the Summer Meeting 2003 at the University of Alberta in Ed- pline at every opportunity and venue. The remarkable work monton. We just learnt the results of the Reallocations exer- accomplished by the staff of the CMS has benefited the en- cise at NSERC. In this operation each GSC and program con- tire Canadian mathematics community. By building on our tributed 10% of its budget to a common pot. The money was strengths, we hope to keep the CMS the same useful tool that then reallocated between the different programs and GSCs. has served us so well over the past 57 years. The GSCs 336 and 337 have contributed $979,000 and have On behalf of all congress participants, I would like to received $1,075,000, i.e. about 9.5% more than what they thank Laval University, which hosted the CMS Summer have contributed. The three Institutes nearly got the parity Meeting, Claude Levesque,´ the meeting’s scientific chair, and the money contributed to the Institutes increased sig- Jean-Pierre Carmichael, president of the local organizing nificantly. These results show the vitality of our discipline. committee, and all their teams, as well as the CMS staff. It also shows our success in making its importance recog- With 400 participants, this was the largest meeting ever held nized: indeed more than half the GSCs lost money in the by the CMS, except for the MATH 2000 summer meeting Exercise. We are very thankful to our colleagues who pre- at McMaster, which was organized jointly with several other pared the application of the mathematical community in the societies. The meeting featured 14 symposia and culminated Reallocations exercise. in the presentation of an honorary doctorate to Robert Lang- I look forward to working over the next two years with lands. This ceremony was held at the Museum of Quebec you, the members of the Canadian mathematics community and was followed by a banquet. We also had the pleasure and the staff of the CMS, as we strive to promote the ad- of recognizing the accomplishments of Priscilla Greenwood, vancement of mathematical sciences.

32 NOTES de la SMC SEPTEMBER/SEPTEMBRE

Math in Moscow Scholarships Update

NSERC and the CMS are pleased to announce a new joint Recently, the Independent University of Moscow created scholarship programme. Beginning this fall, three schol- a new program, MATH in MOSCOW, offering foreign stu- arships of $10,000 each will be awarded annually to sup- dents (undergraduate or beginning graduate students special- port three Canadian students registered in a mathematics or izing in mathematics and/or computer science) the chance to computer science program to attend a semester at the Math spend a semester in Moscow studying within its MATH in in Moscow program (undergraduate or beginning master’s MOSCOW program (www.mccme.ru/mathinmoscow). The level). courses are taught in English. Besides mathematics courses, One scholarship will be awarded in the fall competition a Russian language course and a course in the history of (application deadline September 30) and two scholarships in Moscow (in English) will be proposed. For those who know the spring competition (deadline April 15). Details can be enough Russian, courses in Russian literature and history (in found at www.smc.math.ca/bulletins/Moscow web.html Russian) will also be available. The list of math courses men- The Independent University of Moscow (IUM) is a small, tioned above includes two courses in theoretical computer elite institution of higher learning focusing primarily on science. mathematics. It was founded in 1991 at the initiative of a The MATH in MOSCOW program provides a fifteen- group of well known Russian research mathematicians, who week-long research experience for students, not only with now comprise the Academic Council of the University. Pro- other mathematically talented and highly motivated under- fessors Pierre Deligne and Robert McPherson, both perma- graduates but also with some of the world’s leading mathe- nent members of the Institute for Advanced Study in Prince- maticians.. Students will be learning mathematics in an envi- ton, also played crucial roles in founding the Independent ronment similar in spirit to that of an NSERC summer schol- University. The American Mathematical Society has had a arship, but with much broader representation from a world- special (although not official) relationship with the institu- class international community. There are few better ways to tion as well, arranging for help in obtaining publications and prepare our most talented undergraduates for further work in helping financially during one especially difficult period. mathematics.

(PRESIDENT–continued from page 1) d’entre nous ont decouvert´ le plaisir de tenir une conversa- Pendant les prochaines annees´ la Societ´ emath´ ematique´ du tionenfranc¸ais avec nos collegues` des autres provinces. Au Canada va continuer a` se mettre au service de la commu- niveau des activites´ pleni´ eres` deux conferences´ ont eu lieu en nautemath´ ematique´ canadienne et a` promouvoir notre dis- franc¸ais, soit la conference´ publique de Jean-Marie de Kon- cipline dans tous les milieux et forums. Le personnel de la inck et la conference´ pleni´ ere` de Robert Langlands. Au ban- Societ´ emath´ ematique´ du Canada fait un travail remarquable quet nous avons pu apprecier´ que Bernard Hodgson mani- qui profite a` toute la communautemath´ ematique´ canadienne. ait l’humour aussi bien en anglais qu’en franc¸ais. Plusieurs En construisant sur nos forces nous pouvons esperer´ main- etudiants´ sont venus au congres` et ont present´ e´ des communi- tenir en la Societ´ emath´ ematique´ du Canada l’outil qui nous cations.Jonathan Borwein vient de terminer son mandat ala` a si bien servis depuis 57 ans. presidence´ de la SMC. Au nom de la Societ´ emath´ ematique´ Au nom de tous les congressistes il me fait plaisir de re- du Canada il me fait plaisir de le remercier pour le travail re- mercier l’Universite´ Laval qui a accueilli la reunion´ d’et´ e´ marquable qu’il a accompli pour la SMC et la communaute´ de la SMC, Claude Levesque,´ president´ scientifique de la mathematique´ canadienne depuis de nombreuses annees´ et reunion,´ Jean-Pierre Carmichael, president´ du comite´ local plus specialement´ pendant sa presidence.´ d’organisation et leurs equipes´ ainsi que le personnel de la Jonathan Borwein s’est investi dans tous les dossiers SMC. Avec 400 participants cette reunion´ est la plus nom- de la SMC: publications, services electroniques,´ education,´ breuse que la societ´ e´ ait organisee´ si l’on exclut la reunion´ recherche, affaires internationales. Outre son action remar- d’et´ e´ MATH 2000 a` McMaster que nous avons organisee´ en queee´ dans ces dossiers Jonathan Borwein a travaille´ dans partenariat avec d’autres societ´ es.´ La reunion´ a compte14´ l’ombre alasant` e´ de la SMC: gestion du personnel adminis- sessions speciales´ et a culmine´ avec la remise d’un doctorat tratif, problemes` de locaux pour la SMC, levee´ de fonds pour honoris causa a` Robert Langlands: la cer´ emonie´ a eu lieu au equilibrer´ les budgets, etc. Dans chaque cas la SMC a pu musee´ du Quebec´ et a et´ e´ suivie du banquet. Nous avons profiter de sa vision globale des problemes` et de son travail eu le plaisir d’honorer Priscilla Greewood, recipiendaire´ du acharne´ pour les resoudre.´ Prix Krieger-Nelson et Edwin Perkins, recipiendaire´ du Prix Nous commenc¸ons une nouvelle annee.´ Voici quelques- Jeffery-Williams de la Societ´ e.´ Le caractere` franc¸ais de la uns de nos activites´ speciales.´ Ce sera la premiere` annee´ ville de Quebec´ a deteint´ sur le congres` si bien que plusieurs du programme “CRSNG-SMC Math a` Moscou”. Les 16-

33 SEPTEMBER/SEPTEMBRE CMS NOTES

18 mai 2003 se tiendra a` l’UQAM le Forum national sur parite.´ De plus leur enveloppe globale a connu une tres` forte l’enseignement mathematique.´ La reunion´ d’hiver 2002 se hausse. Ces resultats´ temoignent,´ non seulement de la vi- tiendra a` Ottawa et la reunion´ d’et´ e´ 2003 a` l’Universite´ talite´ de notre discipline mais de notre capacite´ comme com- d’Alberta a` Edmonton. munaute´ a` faire reconnaˆıtre son importance: en effet plus de Au moment de mettre sous presse nous venons la moitie´ des comites´ ont vu leur enveloppe baisser . Nous d’apprendre les resultatset´ programme de l’exercice de sommes reconnaissants a` nos collegues` qui ont prepar´ ele´ reallocation´ au CRSNG. Dans cet exercice chaque comite´ dossier de defense´ des mathematiques´ dans l’operation´ de contribuait 10% de son enveloppe. La somme ainsi collectee´ reallocation.´ etait´ ensuite redistribuee´ entre les differents´ comites.´ Les Je me rejouis´ de travailler pendant les deux prochaines comites´ 336 et 337 ont ainsi contribue´ 979,000$ et se sont annees´ avec vous, membres de la communautemath´ ematique´ vus attribues´ 1,075,000$, soit environ 9.5% de plus que ce canadienne et membres du personnel de la SMC, a` qu’ils ont contribue.´ Les trois Instituts ont obtenu la quasi- l’avancement des sciences mathematiques.´

CALL FOR NOMINATIONS / APPEL DE CANDIDATURES

Various committees of the CMS have been served throughout Un grand nombre de membres de la Societ´ emath´ ematique´ the years by many members of the Canadian mathematical du Canada ont sieg´ e,´ a` titre ben´ evole,´ aux divers comites´ de community on a voluntary basis. The Society is grateful to la Societ´ e´ au fil des ans. La Societ´ e´ remercie toutes ces per- all its memebers for their time and generous support. sonnes de leur temps et de leur gen´ erosit´ e.´ For the year 2003, we will have vacancies on the follow- Pour l’annee´ 2003, nous aurons des postes vacants au ing committees: sein des comites´ suivants : –Advancement of Mathematics Committee –Comite´ pour l’avancement des mathematiques´ –Education Committee –Comited’´ education´ –Electronic Services Committee –Comite´ des services electroniques´ –Endowment Grants Committee –Comite´ d’attribution des bourses du fonds de dotation –Finance Committee –Comite´ des finances –International Affairs Committee –Comite´ des affaires internationales –Mathematical Competitions Committee –Comite´ des concours mathematiques´ –Publications Committee –Comite´ des publications –Research Committee –Comite´ de recherche –Student Committee –Comite´ des etudiants´ –Committee On Women in Mathematics –Comite´ des femmes en mathematiques´

We warmly invite nominations for memberships on these Nous encourageons fortement les membres de la commu- committees by members of the Canadian mathematical com- nautemath´ ematique´ canadienne a` proposer des candidats aux munity. Nominations should include full addresses, e-mail comites´ ci-dessus. Les mises en candidature doivent com- addresses and a brief rationale and be submitted to the ad- porter l’adresse postale complete` du candidat et son adresse dress below by October 1, 2002. de courriel, ainsi qu’une breve` justification de la mise en can- Descriptions of roles of the above committees may be didature, et parvenir a` l’adresse ci-dessous au plus tard le 1er found in http://www.cms.math.ca/Docs/Terms/TofRef/. octobre 2002. Vous trouverez la description des rolesˆ des comites´ sus- mentionnes´ au http://www.cms.math.ca/Docs/Terms/TofRef/.f (anglais seulement).

Chair of Nominating Commitee President´ du Comite´ des mises en candidature Canadian Mathematical Society Societ´ emath´ ematique´ du Canada 577 King Edward, Suite 108 577 King Edward, Suite 108 POB 450, Station A CP 450, Succursale A Ottawa, Ontario CANADA K1N 6N5 Ottawa (Ontario) CANADA K1N 6N5 [email protected] [email protected]

34 NOTES de la SMC SEPTEMBER/SEPTEMBRE

REALLOCATION AND MATHEMATICS by Richard Kane, Chair, Mathematics Steering Committee

(I) Leadership Support Supplements to make a common submission. This was the case for the two This refers to Proposal A, intended to provide “additional Mathematics GSC’s. The Mathematics Steering Committee funds to promote structured initiatives by recognized lead- has a website www.math.ualberta.ca/nserc/ ers”. This money will be awarded selectively to augment the Each discipline submission was expected to satisfy the Research Grants of selected individuals. following format. (1.) A vision for the discipline in Canada, Implementation of this supplement program is compli- presented in an international context. (2.) Strategy for the cated by the fact that the amount awarded is considerably less future development of the discipline. (3.) Specific practical than the amount requested ($1M) in the proposal submitted proposals to implement the strategy over the four year period to NSERC. The available funding will only support a much 2003-2006. (4.) Consequences of no reallocated funds. (5.) more limited program than was envisaged. The question of Implementation of the last exercise. implementation is already being discussed by NSERC and It is clear from the comments of the Reallocation Com- the chairs of the Mathematics GSC’s. (e.g. average amount mittee on the various submissions that one ignored this for- to be awarded? one time competition covering grantees from mat at one’s own peril. It was crucial to present a clear all four years of the grant cycle?) Since this funding covers “vision” and to develop a strategy with funding proposals the next four funding competitions, decisions will have to be strongly connected to the vision. made quickly and then communicated, so that those applying The three Mathematics Institutes each made their own in- for renewal in the fall will know the rules. dependent submissions. However, the three Institute Direc- (II) Guide to Reallocation Information tors were also members of the Mathematics Steering com- The NSERC website contains comprehensive infor- mittee and helped prepare that document as well. mation about the Exercise and its outcome. This in- The Mathematics submission contained three (ranked) formation can be accessed via the NSERC main page funding proposals. The proposals were: www.nserc.ca/index.htm. The actual site for obtaining in- PROPOSAL A: Additional funds to promote structured formation is initiatives by recognized leaders in the community during the www.nserc.ca/programs/real2000-e.htm period 2003-2007; this requires $50K for each of 20 leaders, The following items are particularly relevant. amounting to $1M per year. (1) For the overall NSERC Report on the 2002 Realloca- PROPOSAL B: Additional funds to enhance the re- tion Exercise go to website search and training capabilities of emerging leaders during www.nserc.ca/programs/real2000/report final e.htm the period 2003-2007; this requires $10K for each of 60 (2) For a clear table listing all the results of Reallocation younger researchers, amounting to $600K. go to website PROPOSAL C: Additional funds for 100 projected new www.nserc.ca/programs/real2000/annex a e.htm. grantees and 40 senior news during the period 2003-2007. (3) For a summary of the funding proposals submitted by This requires $16.5K for each of 100 new applicants and the various disciplines go to website $33K for each of 40 senior news, amounting to a total of www.nserc.ca/programs/real2000/annex b e.htm $2.97M per year. (4) For the complete submissions of the various disci- (IV) Reallocation Results plines go to website Of the 19 GSC submissions to Reallocation only 6 re- www.nserc.ca/programs/real2000/subs e.htm sulted in increased funding for the disciplines involved. The (5) For the comments of the Reallocation Committee on chart mentioned in Part II above presents a clear picture. the discipline submissions go to website With the exception of Electrical Engineering these submis- www.nserc.ca/programs/real2000/feedback e.htm sions came from the the Mathematical and Physical Sciences. (III) The Mathematics Submission Mathematics was one of them. The Mathematics GSC’s con- The following is a brief summary of the outcome of Re- tributed $979K to the Reallocation pot and received $1075 allocation from the vantagepoint of Mathematics. This is the back. The funding was awarded as follows: third such Reallocation process. All NSERC Grants Selec- Proposal A $270 tion Committees, as well as the institutes funded by the Re- Proposal B $0 search Grants program, (CITA, CRM, Fields Institute, PIMS) Proposal C: $805 contributed 10% of their NSERC budgets to a pot for redis- tribution. The money was awarded by the Reallocation Com- Proposal A was the most difficult one for the Steering mittee on the basis of funding proposals submitted by the var- Committee to come to grips with. The Reallocation Com- ious disciplines. In a number of cases, two GSC’s combined mittee described it as “innovative” and “well received”. One

35 SEPTEMBER/SEPTEMBRE CMS NOTES rationale provided for rejecting Proposal B was that it signif- to the Reallocation pot and received $674K in return. All icantly overlapped Proposal C. three institutes are now equally funded by NSERC with each The three Mathematical Institutes were highly praised receiving $970K per year. As well, a joint project of the by the Reallocation Committee, and their combined NSERC three Institutes with the Statistics community will be funded funding was increased significantly. They contributed $247K at $172K per year.

34th CANADIAN MATHEMATICAL OLYMPIAD WINNERS

A total of 81 students from 47 Canadian schools were in- lik, Queen Elizabeth High School, Halifax, Nova Scotia; vited to write the 2002 CMO based upon their performance in Cornwall Lau, David Thompson Secondary School, Vancou- the 2001 Canadian Open Mathematics Challenge, the CMS ver, British Columbia; Tian Feng, Vincent Massey Secondary Correspondence Training Programme and other mathematics School, Windsor, Ontario; Yang Yang, Don Mills Collegiate competitions. Students had to solve five difficult questions Institute, Toronto, Ontario. during the three hour 2002 CMO examination held on March More than 4,000 students wrote the 2001 Canadian Open 27, 2002. Mathematics Challenge and the winners of the 2001 Open “To be an olympiad winner is a remarkable achievement” and the 2002 CMO were honoured at a CMS Awards Ban- said Dr. Daryl Tingley, University of New Brunswick at quet held at the University of Waterloo in June. Fredericton, and Chair of the CMS Mathematical Compe- The Society receives major support from Sun Life Fi- titions Committee. “A real benefit of contests like the CMO nancial. Other sponsors include: the Ministry of Education, is the motivation it gives students to explore problems not Ontario; the Ministry of Education, Quebec; Alberta Learn- encountered in a standard school curriculum. It also helps ing; Department of Education, New Brunswick; Department students gain a greater understanding and appreciation of the of Education, Newfoundland and Labrador; Department of role of Mathematics in the workplace.” Education, Northwest Territories; Department of Education First Prize and the Sun Life Financial Cup went to Tianyi Saskatchewan; the Department of Mathematics and Statis- Han, Woburn Collegiate Institute, Toronto, Ontario. Sec- tics, University of New Brunswick at Fredericton; the Cen- ond Prize went to Roger Mong, Don Mills Collegiate In- tre for Education in Mathematics and Computing, University stitute Toronto, Ontario. Third Prize went to Paul Cheng, of Waterloo; the Department of Mathematics and Statistics, West Vancouver Secondary School, West Vancouver, British University of Ottawa; the Department of Mathematics, Uni- Columbia. Honourable Mentions were awarded to Robert versity of Toronto; Nelson Thomson Learning and John Wi- Barrington Leigh, Old Scona Academic High School, Ed- ley and Sons Canada Ltd.. monton, Alberta; Olena Bormashenko, Don Mills Colle- giate Institute, Toronto, Ontario; Xiaoxuan Jin, Vincent Problems, solutions and other contest information can be Massey Secondary School, Windsor, Ontario; Timothy Kusa- found at: www.cms.math.ca/Competitions/CMO/

Left to right Mark Heritage, (Head of Mathematics, Woburn Collegiate Institute), Ed Barbeau,(University of Toronto), Stewart Martin, (Sun Life Financial), and Tianyi (David) Han.

36 NOTES de la SMC SEPTEMBER/SEPTEMBRE

(Steering Committee Report–continued from page 4) and therefore potential NSERC grantees. This rapidly grow- ing strength of the discipline is reflected in the 10% rise in (ii) the 1998 mathematics submission provided a list of ”31 the number of grantees in GSC 336/337 in the past two years younger researchers at the forefront of exciting emerging (DD, Table 1). The number of new applicants for the past 3 fields.” grant competitions (including the present one) are 47, 47, and In the past 4 years, the total value of the grants of 52, respectively; these totals include 12, 13, and 23 senior these young researchers rose more than 50% from $503K to news, respectively. This demographic surge will continue. $777K; and (iii) providing more money for the support of For example, 42 tenure track positions for mathematicians postdoctoral fellows (PDFs) was an implicit goal of the 1998 are advertised for the coming year; 14 of these are at the funding requests. There has been a striking increase (over level of associate professor or higher. The Canada Research 50%) in research grant expenditures on PDFs over the past 3 Chairs (CRC) program will also have considerable impact years (HQP, Table 16), reflecting the additional funding pro- on mathematics departments, and hence on GSCs 336/337, vided for key researchers. Moreover, these expenditures have in the next few years. A survey of Canadian mathematics de- been leveraged by at least 100% - almost all mathematics partments yields commitments for 31 CRCs over the next 5 PDFs are financed by partnering research funds with other years, evenly spread between Tier I and II; 10 CRC positions sources. are presently being advertised. The current 9 CRCs funded Discipline Dynamics through GSC 336/337 have an average grant of over $41K. Several dynamics in Canadian mathematics have shaped our perception of the precise funding proposals to be pur- These demographics are wonderful news for Canadian sued. These discipline dynamics are detailed here. mathematics and its future, but a mixed blessing for GSCs (a) Larger Scale Research and Training: The existence 336/337. An influx of new talent raises serious concern about of groups directed towards targeted, very often interdisci- the ability of these GSCs to provide adequate grants for all of plinary, areas of research is familiar to the experimental sci- these deserving new applicants over the next few years with- ences, but is a new and rapidly expanding phenomenon in out seriously under-funding many strong researchers cur- mathematics. There are many forces encouraging and shap- rently receiving grants. The scale of this concern has led us ing such groups, such as: to submit a separate funding proposal for new applicants. (c) Increased Funding Needs: The funding needs of • the active support of the mathematical institutes or MI- mathematicians are intensifying. As increasing numbers of TACS; mathematicians become involved in larger scale research • the growing emphasis on interdisciplinary activity. (e.g., leading an active group or directing an expensive There is an increasing complexity to research projects project), there is an urgent need for significantly more fund- having a well-defined mathematical component, re- ing. There is also a collective need for more funds. As al- sulting in an expanded need for professional expertise ready noted, a large number of young talented researchers and PDF support; are entering the system; however, it will be shown (see Part 7) that many excellent researchers currently in the system • the surge in university-based labs targeting the private will not be leaving. Funding an increasing number of active sector; and researchers requires more money. In addition, current fund- ing levels in mathematics are too low to adequately support • the drive within Canadian universities to define re- the necessary numbers of HQP. The current average grant of search and training priorities and to establish long- $16,580 (only $2,250 above what it was a decade ago) (DD, term hiring plans that reflect those priorities. Table 3) supports at most one Masters student per year. Even larger grants in mathematics cannot support a full PDF; the This phenomenon has had a substantial cumulative effect. importance of PDFs in mathematical research programs will Typically, this research format is built around a leader and be emphasized in Part 6. For the information of our refer- involves a combination of PDFs, programming and techni- ees, we point out that university support of HQP in Canada cal assistants, graduate students, university researchers, and is typically limited to salary provided by sessional teaching visitors. Such groups provide wonderfully stimulating train- and TA duties. Research grants are a necessary and major ing grounds (and magnets!) for these graduate students and component of HQP support. PDFs. This model for the mathematics community is cre- ating a need to finance such leaders at a level beyond that Three Funding Proposals previously available for single individuals. We have developed 3 funding proposals based on these (b) Demographic Pressures: The current turnover in uni- current impacts and on future trends in Canadian mathemat- versity faculty is producing a rapid increase in the fraction of ics. For each, we give the rationale followed by the funding university mathematicians who are strong active researchers request.

37 SEPTEMBER/SEPTEMBRE CMS NOTES

(a) Leadership Support: There is a new discipline dy- (c) New Applicants: The demographic statistics pre- namics in mathematics–group-based research is being car- sented above strongly suggest that the number of grantees ried out on a larger scale than ever before. There are now both in GSCs 336/337 will increase sharply over the next 4 years very effective established groups and a number of emerging and that, on a yearly basis, GSCs 336/337 will need to award groups, each centered around key individuals. Examples of 35-40 new grants, including at least 10 to senior new appli- such groups and their activities are to be provided in Part 3. cants. Added resources are required for existing groups to realize The current average grant in mathematics for junior new their full potential and for fledging groups to evolve to a more applicants is $11K. This is a minimal entry grant whose level structured level. The local presence of adequate funding is a is ultimately explained by the current low value of mathemat- primary reason for the existence of the existing groups where ics grants. The target should be to award junior newcomers they have emerged. Notably, the evolution of group activity the current average grant in mathematics, namely $16.5K. is more pronounced in Quebec and western Canada. The activity level of new grantees easily warrants such entry It is essential for Canadian mathematics that we support grants. As a comparison, this is almost exactly the average and encourage this new type of dynamic and the leaders who entry grant over the past 4 years in Computing Science (DD, are driving it. To do so, GSCs 336/337 must provide targeted Table 15), which is a group of beginning researchers with funding to recognized researchers who are assuming, or have similar funding needs. The funding needs of senior new ap- assumed, a leadership role involving an active group, typi- plicants, because of their consistently high level of activity, cally focused on training or a major research project. Such will average twice (e.g., $33K) that of junior new applicants. funds would provide resources to allow researchers to carry We have also used NSERC’s own data to analyze the sit- out a structured initiative. To have a real impact, at least 20 uation regarding new applicants for GSCs 336/337 (see Part leaders require targeted funds with an average value of $50K 7). The analysis leads to two conclusions: per year, normally awarded for a 4 year period. Important (1) About 25 new grantees per year will apply to GSC criteria would be demonstrated need and a credible plan for 336/337. This definitely contrasts with the GSC reality of 47, pursuing alternative funding in the case of longer-term activ- 47, and 52 new applicants in the last 3 competitions. More- ity. Awards could either be part of the normal grant cycle or over, NSERC data does not take into account senior new ap- be dispersed in a special competition. plicants. Proposal A: Additional funds to promote structured initia- (2) The money to become available for redistribution via tives by recognized leaders in the community during the pe- attrition in GSCs 336/337 will essentially equal the contri- riod 2003-2007; this requires $50K for each of 20 leaders, bution of 10% of GSCs 336/337 budget to the Reallocation amounting to $1M per year. Exercise. Without funding provided by Reallocation, GSCs (b) Emerging Leaders: There is an impressive number of 336/337 will have no funds to finance grants for new appli- junior researchers in both traditional and emerging areas with cants, unless funding levels of renewal grantees is signifi- high impact and visibility, and who must be funded in pro- cantly reduced. portion to their activity. These rising stars can be identified as grantees seeking their first or second renewal who have a dis- Taking into account the major divergence between actual tinguished research record of at least 6-10 years duration. At empirical data and the estimate arrived at from NSERC data, that stage, a better assessment of quality and financial needs we are projecting 35 new grantees per year, including 10 se- can be made. These emerging leaders also have growing fi- nior grantees. nancial needs, particularly with respect to training of HQP. Proposal C: Additional funds for 100 projected new grantees Proposal B: Additional funds to enhance the research and and 40 senior news during the period 2003-2007. This re- training capabilities of emerging leaders during the period quires $16.5K for each of 100 new applicants and $33K for 2003-2007; this requires $10K for each of 60 younger re- each of 40 senior news, amounting to a total of $2.97M per searchers, amounting to $600K. year.

ICM 2002 Medallists

At the opening ceremony of ICM 2002 on August 20th, Chinese President Jiang Zemin and Jacob Palis, President of the International Mathematical Union, awarded Fields Medals to France’s Laurent Lafforgue and Vladimir Voevodsky from Russia. Madhu Sudan from the Massachusetts Institute of Technology won the Nevanlinna Prize. Laurent Lafforgue, of the IHES, Bures-sur-Yvette, was honoured for making major advances in the Langlands Program, which conjectures certain deep connections among number theory, analysis and group representations. Vladimir Voevodsky, IAS Princeton, was cited for developing a new cohomology theory for algebraic varieties. The Nevanlinna Prize recognizes exceptional work in theoretical computer science.

38 NOTES de la SMC SEPTEMBER/SEPTEMBRE

OBITUARY / AVIS DE DEC´ ES` Richard Brown 1941-2002

the conference and periodical literature on the programming language J. This followed on a long-time interest in APL, and tied in with his teaching interests in optimization and theory of interest. During his last sabbatical at CU-Denver, Richard collaborated with three University of Colorado researchers on numerical models in population genetics. He brought the power and efficiency of J to bear on these problems, writ- ing extremely compact and general codes that out-performed then existing ones. In the 1970s, Richard introduced a course in game the- ory at the first year level. This proved to be very popular and filled a niche for a number of years at a time when York Colleagues in the Department of Mathematics and Statistics discouraged early specialization in the undergraduate pro- at York University mourn the recent death of well-loved col- gram. As more applied programs became the norm, Richard league Richard Brown. quickly adapted to the new needs, making major contribu- Richard Laurence Wilmott Brown, the eldest of three tions to courses in operations research, business mathemat- sons of Laurence Wilmott Brown and Vivian Eliza Brown ics and, in general, to computer use in our courses. Never an (nee Kyle), was born in Ottawa on September 17, 1941. empire-builder, he did not seek credit for those of his ideas He was educated at Nepean High School and at Carleton picked up by others, and did not cling to ideas that had fallen University, where he received an Honours BSc degree in out of favour, choosing rather to pursue new ones. Mathematics in 1962. In the same year he was awarded a With the increase of computer use in the 1980s, Richard Woodrow Wilson Fellowship. A fellow Carleton student re- was a constant source of help and advice to his colleagues. members him as brilliant and unassuming. He went to Har- He even started a “Computer Users Newsletter” which was vard University as a graduate student and obtained his PhD just what was needed at the time. He had a fondness for keep- under the supervision of Barry Mazur in 1969 with a thesis ing things elegantly simple and loved to show that a clever entitled“Cobordism, Embeddings, and Fibrations of Mani- idea could do the job of some bloated software. He served the folds”. While at Harvard, Richard married fellow graduate Department well as Undergraduate Director during the years student Julia May Nowlin. Richard and Julia (also a Harvard 1987-1992. Richard made an enormous contribution to both PhD in Mathematics) became faculty members at York, in York and the Canadian Mathematical Society by serving as 1969 and 1970, respectively. They have been excellent col- Chair of the York Local Arrangements Committee for the In- leagues whose dedication, loyalty and performance showed ternational Mathematical Olympiad in 1995. This simple ti- their commitment to the true purposes of the University. tle does not do justice to what was an incredibly arduous task Richard’s early research work was in differential topol- extending over a number of years. That Richard was asked to ogy. The published results of his thesis were quoted and used do it was a testimony to the confidence placed in him by his by others including R. L. Cohen in his work on the immer- colleagues. The success of this, the only IMO ever hosted by sion conjecture (Ann. of Math. 122 (1985), 237-328). His Canada, was directly attributable to his leadership skills in early work continues to be of interest and is quoted in re- this huge undertaking. Richard was quiet and unpretentious. views of recent articles by Y. Kuramoto, Y. Kuramoto and Better acquaintance revealed that he had some strong views T. Yasui, and by I. Takata. But it would have been out of but it was observed that rarely, if ever, did he say an unkind character for Richard to continue to exploit a single area. He or critical word about anyone. It was as if he knew that life had the knack of extracting the essence from a mathematical is too short for quarreling and that time should be spent in result or application and presenting it in a context that any- constructive ways. one could understand. He would illustrate some concepts in In summer 2001, Richard was diagnosed with cancer. He catastrophe theory with a model of wood and elastic. His arti- bore his suffering patiently but not passively (he studied the cle entitled “The Klein bottle as an eggbeater”, Mathematics literature on cancer, including current developments) until Magazine 46 (1973), 244-250 is a good example of his ap- his death on March 9, 2002. He leaves his wife Julia and proach. Often he adapted his interests to those of the people three children, Daniel, Amanda and Emily. May their pain be around him. For example, a sabbatical leave at the University eased by the knowledge that dozens of colleagues and thou- of Sussex led to a joint paper with John Maynard Smith on sands of students cannot fail to have been influenced by his competition and body size. In recent years, he contributed to genius, helpfulness and dedication.

39 SEPTEMBER/SEPTEMBRE CMS NOTES

NEWS FROM DEPARTMENTS

Acadia University, Wolfville, NS Applied Sciences (which includes Mathematics) for the pe- Appointments: Nancy Clarke (Assistant Professor, riod July 2001 to June 2003. tenure track, Graph Theory, July 2002), Jianan Peng (As- sistant Professor, tenure track, Statistics, July 2002), Hol- University of British Columbia, Vancouver, BC ger Teismann (Assistant Professor, tenure track, Differential Appointments: Ailana Fraser (Assistant Professor, Dif- Equations, July 2002) Marco Pollanen (Assistant Professor, ferential Geometry, July 2002); Alexander Holroyd (Assis- fixed term, Probability, July 2002). tant Professor, Probability, July 2002); Rachel Kuske (Asso- Retirements: Vincent Leung (retired June 30, 2002), ciate Professor, Industrial Applied Mathematics, July 2002); who taught in the department for 35 years; Jag Chawla, Vlada Limic (Associate Professor, Probability, July 2002); (June 2002) a statistician who joined the department in 1986; Jozsef Solymosi (Assistant Professor, Probability, Combina- Michael Nutt, (June 2002), who joined Acadia in 1975. torics, July 2002);Tai-Peng Tsai (Assistant Professor, Partial Visitors: R. Shonkwiler, USA (Georgia Tech), Mathe- Differential Equations,July 2002); Stephanie van Willigen- matical Biology, Stochastic Optimization, Parallel Process- burg (Assistant Professor, Discrete Mathematics , July 2002). ing will be a visiting Professor in the Fall term 2002; S. Kang, Promotions: Jim Bryan (Associate Professor with Tenure); Canada (Toronto), Biostatistics,McGill University, Montreal. Michael Doebeli (Associate Professor with Tenure); Izabella Other News: Paul Cabilio has returned as Head. Laba (Tenure). Dalhousie University, Halifax, NS Resignations: Changfeng Gui (June 30, 2002). Award: Matiur Rahman has received an “Eminent Sci- Retirements: An Ton Bui (June 30, 2002). entist” medal, awarded by the Wessex Institute of Technol- Awards and Distinctions: Priscilla Greenwood (Professor ogy (UK) for outstanding contributions to fluid mechanics. It Emeritus, 2002 Krieger-Nelson Prize); Leah Keshet (Poster was presented at the Fourth International Conference on Ad- awards at MITACS AGM (May 2002) and Faculty of Sci- vances in Fluid Mechanics held at Ghent, Belgium in May. ence Achievement Award 2002); Izabella Laba (University McGill University, Montreal, QC Faculty Award 2000-2005, Faculty of Science Achievement Appointments: Antony Humphries (Associate Professor, Award 2002); Greg Martin (Lester R. Ford Award from numerical analysis, July 2002); Alexei Miasnikov (Profes- AMS, June 2002); Edwin Perkins (2002 Jeffery-Williams sor and CRC Chair, group theory, July 2002); Ravi Ramakr- Prize Lecture, 2001-02 Science Teaching Award); Vinayak ishna (Associate Professor, number theory, July 2002); Rus- Vatsal (Alfred P. Sloan Research Fellow 2002-2004); Ailana sell Steele (Assistant Professor, Statistics, July 2002). Fraser (NSERC University Faculty Awards 2002); Stephanie Promotions: Eyal Goren (Associate Professor with van Willigenburg (NSERC University Faculty Awards 2002). tenure, June 2002); Sherwin A. Maslowe (Emeritus Profes- Visitors: Martial Agueh (USA, Calculus of Varia- sor, September 2002). tions, (Sept.2002-Aug.2003); Kevin Buhr (USA, Probabil- Awards: Henri Darmon (NSERC Stacie Fellowship); ity, Jan.2002-Dec.2003); Temeur Chaolu (China, Symme- Michael Makkai (Thompson award for excellence in grad- tries of Partial Differential Equations, March 2002-March uate supervision and teaching). 2003); Jaydeep Chipalkatti (Canada, Algebraic Geometry, Memorial University of Newfoundland, St. John’s, NF Sept.2002 - Aug.2004); Nima Geffen (Israel, Fluid dynam- Promotions: David Pike (Associate Professor, Septem- ics, June 2002 - June 2003); Hamidani Hamideh (Iran, Proba- ber 2002); Xiao-qiang Zhao (Associate Professor, September bility, Aug.2002 -July 2003); Kiumars Kaveh(Canada, Alge- 2002); Xingfu Zou (Associate Professor, September 2002). braic Geometry, Sept.2002 - Aug.2004); Euiwoo Lee (Korea, Tenure: Serpil Kocabiyik (September 2002). Mathematical Biology, Aug 2002- Aug 2003); Sheng Liu Retirements: Roland Eddy (August 2002); Bruce (China, Partial Differential Equations, June 2002-Dec.2002); Shawyer (August 2002); Sankatha Singh (August 2002). Nathaniel Newlands (Canada, Mathematical Biology, April Awards/Distinctions: Xingfu Zou, Young Innovators 2002-April 2003); Michael Novak (Canada, Soil Physics, Award 2002. Sept.2002-Dec.2003); Changzheng Qu (China, Symmetry Groups, Sept.2002 -Aug.2003); Yanxia Ren (China, Markov UniversiteLaval,Qu´ ebec,´ QC Process, July 2002 - Dec.2002); Ramajayam Sahadevan Promotion:Michel Fortin(Emeritus Professor,June 2002). (India, Nonlinear Differential and Difference Equations, University College of Cape Breton, Sydney, NS Sept.2002-Dec.2002); Akira Sakai (Japan, Mathematical Appointment: George Chen (Lecturer, September 2001). Physics, Sept.2000 - Dec.2002); Joern Sass (Germany, Math- Promotion: Edmund Rudiuk (Associate Professor, July ematical Finance, Oct.2001 - July 2003); Alexander Schied 2001). Retirement: Tat Ngai (June 2002). Other News: Dou- (Germany, Financial Mathematics, July 2002-Sept.2003); glass Grant became Chair of the Department of Physical and Nikolaus Vonessen (USA, Algebra, June 2002-Aug. 2003);

40 NOTES de la SMC SEPTEMBER/SEPTEMBRE

Zhenya Yan (China, Nonlinear Partial Differential Equa- July 2002); A. Iovita (Associate Professor, January 2003). tions, Sept.2002-Aug.2003); Zhenbu Zhang(USA, Nonlinear Promotions: J. Garrido (Professor, June 2002); D. Korotkin parabolic and elliptic equations, Sept.2002-Aug.2003). (Associate Professor, June 2002). University of Western Ontario, London, ON University of Guelph, Guelph, ON Appointments(tenure stream): Graham Denham (As- Appointments: Herb Kunze (Assistant Professor, applied sistant Professor, algebraic combinatorics, January 2002); mathematics, 2000); Gerarda Darlington (Assistant Profes- Nicole Lemire (Assistant Professor, NSERC University Fac- sor, Biostatistics, 2000); Heinz Bauschke (Assistant Profes- ulty Award , July 2002). sor, Optimization, 2001); Gary Umphrey (Assistant Profes- Promotion: David Riley (Associate Professor, tenure, sor, Biostatistics, 2001). July 2002). Promotion: Eleanor Chu (Professor, July 2001). Postdoctoral Fellows: Kristine Bauer (Ph.D. Univ. of Retirements: Joe Mokanski. He became a member of the Illinois, homotopy theory, January 2003); Oliver Roendigs department in 1963. A gifted teacher, he won the Univer- (Ph.D. Bielefeld, homotopy theory, algebraic geometry, July sity of Guelph Faculty Association Teaching Award (1990), 2002). Andrew Richardson (Ph.D. Univ. of Illinois, commu- the Ontario Confederation of University Faculty Association tative algebra, July 2002). Award (1992), and the Ontario Lieutenant Governor’s Award Awards/Distinctions:Dan Christensen (Government of for Excellence in Teaching (1992). He was Assistant Chair Ontario Premier’s Research Excellence Award, 2001). from 1982 to 1995, and assumed the Chair in 1995; Hosh Visitors: M. Fiali (Univ. of Oulu, Finland, Analy- Pesotan. He became a member of the department in 1968. sis, Aug.-Dec.2001);P. Hajac (Univ. of Munich, Germany, His research centred around combinatorial aspects of statis- Non-commutative Geometry, March 2002); R. Laubenbacher tical design. He enjoyed teaching a great variety of courses (Virginia Bioinformatics Institute, USA, Homotopy Theory, at all levels and consistently ranked among the highest teach- Computer Science, March 2002); P. Paramonov (Moscow ing evaluations in the department; Robert G. Chapman. He State University, Complex Analysis, May-June 2002); W. joined the department in 1969. He has been a leader in re- Raskind, Univ. of Southern California, Algebraic Geometry, search, teaching and service to the university. He has diverse April 2002); A. Sedletski, Moscow State University, Russia, research interests, from the cohomology of finite groups to Complex Analysis, May-June 2002); P. Shumyatski, Univ. of statistical design. In 1989, he was awarded a University of Brasilia, Brazil, Non-commutative Algebra, January 2002); Guelph Faculty Association Teaching Award. R. Sigurdsson (Univ. of Iceland, Complex Analytic Geome- Deaths: George Leibbrandt, 1938-2001, He was a valued try, Oct.-Nov.2001); B. Toen, Univ. de Nice, France, Alge- member of the Department of Mathematics and Statistics at braic Geometry, Homotopy Theory,April-May 2002). the University of Guelph from 1966 until his untimely death Other News: Vladimir Voevodsky (IAS, Princeton) was in 2001. An applied mathematician specializing in theoreti- the speaker in the Department’s annual Distinguished Lec- cal physics, he published 72 refereed papers and a 1994 re- ture Series, April 25-26, 2002; The University of Western search monograph on Noncovariant Gauges. He was visiting Ontario became a Principal Sponsoring University for the professor at many universities including Cambridge and Har- Fields Institute in 2001, and has recently upgraded its annual vard and twice received Germany’s Alexander von Humboldt contribution to Fields to accomodate an expanded level of Fellowship. More recently, he was a founding director of the shared activity in research and training. This activity includes newly established Perimeter Institute for Theoretical Physics the running of Fields Institute programs at UWO. The first of in Waterloo. these will be a program entitled “Applied Homotopy Theory” Ernie Frejer, He was a founding member of the depart- to be held in the Department of Mathematics at UWO during ment, coming on board in 1965 and retiring in 1994. He the month of September, 2003 under the direction of Rick was a meticulous teacher, always well-organized, clear and Jardine and Dan Christensen. This program will involve long fair. He had the distinction of teaching the greatest variety of term visits by G. Carlsson (Stanford), P. Goerss (Northwest- courses in the department, from first year algebra to fourth ern) J. Morava (Johns Hopkins) and F. Morel (Paris VII), and year tensor analysis. there will be a 5 day conference near the end of the month. Award/Distinction: Gerada Darlington (University of Concordia University, Montreal, Quebec´ Guelph Central Student Association Teaching Excellence Appointments: A. Sen (Assistant Professor, Statistics, Award, 2001).

41 SEPTEMBER/SEPTEMBRE CMS NOTES

CALENDAR OF EVENTS / CALENDRIER DES EV´ ENEMENTS´

SEPTEMBER 2002 SEPTEMBRE 2002 [email protected], 29 Aug–3Polynomial Identities in Algebras (Memorial Uni- http://www:newton.cam.ac.uk/programs/NST/nstw04.html versity of Newfoundland, St. John’s, Newfoundland) JANUARY 2003 JANVIER 2003 http://www:math.mun.ca Jan – Aug Thematic Program on Automorphic Forms, 9–20 Axiomatic, Enriched and Motivic Homotopy Theory (The Fields Institute for Research in Mathematical Sciences, (NATO Advanced Study Institute) (Issac Newton Institute for Toronto) Mathematical Sciences, Cambridge, U. K.) Automorphic@fields.utoronto.ca [email protected], http://www.newton.cam.ac.uk/programs/NST/nstw01.html FEBRUARY 2003 FEVRIER´ 2003 15–21 8th International Conference on General Inequalities 10–15 Mathematiques Appliquees et Applications des Math- (De La Motte Castle, Noszvaj, Hungary) ematiques (Nice, France) [email protected] http://www.acm.emath.fr/amam/ 23–28 Workshop on Categorical Structures for Descent and MAY 2003 MAI 2003 Galois Theory, Hopf Algebras and Semiabelian Categories, 11–16 International Conference on General Control Prob- (The Fields Institute for Research in Mathematical Sciences, lems and Applications (GCP2003) : Dedicated to the 100th Toronto) anniversary of A./ N./ Kolmogorov (Tambov Sate University, [email protected] Tambov, Russia) 29–Oct 3 18th International CODATA Conference (Hotel www.opu2003.narod.ru/ Delta Centreville, Montreal, Que) [email protected], http://www.codata.org JUNE 2003 JUIN 2003 30–Oct 4 K-theory and Arithmetic (Issac Newton Institute 14–16 CMS Summer Meeting / Reunion´ d’et´ edelaSMC´ for Mathematical Sciences, Cambridge, U. K.) (University of Alberta, Edmonton, Alberta) [email protected], Monique Bouchard: [email protected] http://www.newton.cam.ac.uk/programs/NST/nstw01.html 17–21 Fourth Butler Memorial Conference (Uni- versity of Alberta, Edmonton, Alberta, Canada) OCTOBER 2002 OCTOBRE 2002 http://conley.math.ualberta.ca/butler.html 17–19 NCTM Canadian Regional Conference (Regina, 18–21 First Joint Meeting between AMS and Real Sociedad Saskatchewan) Hosted by the Saskatchewan Mathematics Matematica Espanola (Seville, Spain) Teachers’ Society. www.us.es/rsme/-ams/ http://www.nctm.org/, http://mathcentral.uregina.ca/SMTS/ JULY 2003 JUILLET 2003 NOVEMBER 2002 NOVEMBRE 2002 2–3 PIMS Cascade Topology Conference (University of 7–11 Fifth International Congress in Industrial and Applied British Columbia, Vancouver, BC) Mathematics (Sydney, Australia) www.iciam.org 25–28 Fifth International Conference on Monte Carlo and QuasiCarlo methods in Scientific Computing (MCQMC) 27 - Aug. 9 Banach algebras and their applications (Univer- (Singapore, Republic of Singapore) sity of Alberta, Edmonton, AB) http://www.mcqmc2002.math.nus.edu.sg http://www.math.ualberta.ca/ ba03/ ´ DECEMBER 2002 DECEMBRE´ 2002 DECEMBER 2003 DECEMBRE 2003 8–10 CMS Winter Meeting / Reunion´ d’hiver de la SMC 6–8 CMS Winter Meeting / Reunion´ d’hiver de la SMC (Marriott Hotel, Ottawa, Ontario) (Simon Fraser University, Harbour Centre, Vancouver, http://www.cms.math.ca/Events/winter02/index.html British Columbia) Monique Bouchard: [email protected] 9–13 Elliptic Cohomology and Chromatic Phenomena (Eu- roWorkshop, Newton Institute, Cambridge, U.K.) SUMMER 2004 ET´ E´ 2004 [email protected], CMS Summer Meeting / Reunion´ d’et´ edelaSMC´ http://www:newton.cam.ac.uk/programs/NST/nstw04.html (Dalhousie University, Halifax, Nova Scotia) 16–20 Higher Chromatic Phenomena (EuroWorkshop, New- Monique Bouchard: [email protected] ton Institute, Cambridge, U.K.)

42 NOTES de la SMC SEPTEMBER/SEPTEMBRE

JULY 2004 JUILLET 2004 http://www.cms.math.ca/Reunions/Toulouse2004/ 12–15 Toulouse 2004 Joint Meeting of between the DECEMBER 2004 DECEMBRE´ 2004 CMS, Societ´ eMath´ ematique´ de France (SMF), Societ´ ede´ Mathematiques´ Appliquees´ et Industrielles (SMAI) and the CMS Winter Meeting / Reunion´ d’hiver de la SMC Societ´ e´ Franc¸aise de Statistiques (SFDS), (Toulouse, France) (McGill University, Montreal,´ Quebec)´ http://www.cms.math.ca/Events/Toulouse2004/ Monique Bouchard: [email protected]

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43 SPRINGER FOR MATHEMATICS

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